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Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression

June 24, 2019 by Veerendra

Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression

Selina Publishers Concise Mathematics Class 10 ICSE Solutions Chapter 11 Geometric Progression

Geometric Progression Exercise 11A – Selina Concise Mathematics Class 10 ICSE Solutions

Question 1.
Find, which of the following sequence form a G.P. :
(i) 8, 24, 72, 216, ……
(ii) \(\frac{1}{8}, \frac{1}{24}, \frac{1}{72}, \frac{1}{216}\), ……..
(iii) 9, 12, 16, 24, ……
Solution 1(i).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 1

Solution 1(ii).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 2

Solution 1(iii).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 3

Question 2.
Find the 9th term of the series :
1, 4, 16, 64 ……..
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 4

Question 3.
Find the seventh term of the G.P. :
1, \(\sqrt{3}\), 3, \(3 \sqrt{3}\) …..
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 5

Question 4.
Find the 8th term of the sequence :
\(\frac{3}{4}, 1 \frac{1}{2}\) 3, …….
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 6

Question 5.
Find the 10th term of the G.P. :
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 7

Question 6.
Find the nth term of the series :
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 8

Question 7.
Find the next three terms of the sequence :
\(\sqrt{5}\), 5, \(5 \sqrt{5}\), ……
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 9

Question 8.
Find the sixth term of the series :
22, 23, 24, ……….
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 10

Question 9.
Find the seventh term of the G.P. :
[late]\sqrt{3}+1,1, \frac{\sqrt{3}-1}{2}[/latex], ……………..
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 11

Question 10.
Find the G.P. whose first term is 64 and next term is 32.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 12

Question 11.
Find the next three terms of the series:
\(\frac{2}{27}, \frac{2}{9}, \frac{2}{3}\), ………….
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 13

Question 12.
Find the next two terms of the series
2 – 6 + 18 – 54 …………
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 14

Geometric Progression Exercise 11B – Selina Concise Mathematics Class 10 ICSE Solutions

Question 1.
Which term of the G.P. :
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 15
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 16

Question 2.
The fifth term of a G.P. is 81 and its second term is 24. Find the geometric progression.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 17

Question 3.
Fourth and seventh terms of a G.P. are \(\frac{1}{18} \text { and }-\frac{1}{486}\) respectively. Find the GP.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 18

Question 4.
If the first and the third terms of a G.P. are 2 and 8 respectively, find its second term.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 19

Question 5.
The product of 3rd and 8th terms of a G.P. is 243. If its 4th term is 3, find its 7th term.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 20

Question 6.
Find the geometric progression with 4th term = 54 and 7th term = 1458.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 21

Question 7.
Second term of a geometric progression is 6 and its fifth term is 9 times of its third term. Find the geometric progression. Consider that each term of the G.P. is positive.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 22

Question 8.
The fourth term, the seventh term and the last term of a geometric progression are 10, 80 and 2560 respectively. Find its first term, common ratio and number of terms.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 23

Question 9.
If the 4th and 9th terms of a G.P. are 54 and 13122 respectively, find the GP. Also, find its general term.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 24

Question 10.
The fifth, eight and eleventh terms of a geometric progression are p, q and r respectively. Show that : q2 = pr.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 25

Geometric Progression Exercise 11C – Selina Concise Mathematics Class 10 ICSE Solutions

Question 1.
Find the seventh term from the end of the series : \(\sqrt{2}\) , 2, \(2 \sqrt{2}\), ………. 32.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 26

Question 2.
Find the third term from the end of the GP.
\(\frac{2}{27}, \frac{2}{9}, \frac{2}{3}\), ………….. 162
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 27

Question 3.
For the \(\frac{1}{27}, \frac{1}{9}, \frac{1}{3}\), ………… 81;
find the product of fourth term from the beginning and the fourth term from the end.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 28

Question 4.
If for a G.P., pth, qth and rth terms are a, b and c respectively ; prove that :
(q – r) log a + (r – p) log b + (p – q) log c = 0
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 29

Question 5.
If a, b and c in G.P., prove that : log an, log bn and log cn are in A.P.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 30

Question 6.
If each term of a G.P. is raised to the power x, show that the resulting sequence is also a G.P.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 31

Question 7.
If a, b and c are in A.P. a, x, b are in G.P. whereas b, y and c are also in G.P. Show that : x2, b2, y2 are in A.P.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 32

Question 8.
If a, b, c are in G.P. and a, x, b, y, c are in A.P., prove that :
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 33
Solution 8(i).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 34

Solution 8(ii).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 35

Question 9.
If a, b and c are in A.P. and also in G.P., show that: a = b = c.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 36

Question 10.
The first term of a G.P. is a and its nth term is b, where n is an even number.If the product of first n numbers of this G.P. is P ; prove that : p2 – (ab)n.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 37

Question 11.
If a, b, c and d are consecutive terms of a G.P. ; prove that :
(a2 + b2), (b2 + c2) and (c2 + d2) are in GP.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 38

Question 12.
If a, b, c and d are consecutive terms of a G.P. To prove:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 39
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 40

Geometric Progression Exercise 11D – Selina Concise Mathematics Class 10 ICSE Solutions

Question 1.
Find the sum of G.P. :
(i) 1 + 3 + 9 + 27 + ……….. to 12 terms.
(ii) 0.3 + 0.03 + 0.003 + 0.0003 + …… to 8 terms.
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 41
Solution 1(i).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 42

Solution 1(ii).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 43

Solution 1(iii).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 44

Solution 1(iv).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 45

Solution 1(v).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 46

Solution 1(vi).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 47

Question 2.
How many terms of the geometric progression 1+4 + 16 + 64 + ……… must be added to get sum equal to 5461?
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 48

Question 3.
The first term of a G.P. is 27 and its 8th term is \(\frac{1}{81}\). Find the sum of its first 10 terms.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 49

Question 4.
A boy spends ₹ 10 on first day, ₹ 20 on second day, ₹ 40 on third day and so on. Find how much, in all, will he spend in 12 days?
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 50

Question 5.
The 4th and the 7th terms of a G.P. are \(\frac{1}{27} \text { and } \frac{1}{729}\) respectively. Find the sum of n terms of this G.P.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 51

Question 6.
A geometric progression has common ratio = 3 and last term = 486. If the sum of its terms is 728 ; find its first term.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 52

Question 7.
Find the sum of G.P. : 3, 6, 12, ……………. 1536.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 53

Question 8.
How many terms of the series 2 + 6 + 18 + ………….. must be taken to make the sum equal to 728 ?
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 54

Question 9.
In a G.P., the ratio between the sum of first three terms and that of the first six terms is 125 : 152.
Find its common ratio.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 54

Question 10.
Find how many terms of G.P. \(\frac{2}{9}-\frac{1}{3}+\frac{1}{2}\) ………. must be added to get the sum equal to \(\frac{55}{72}\)?
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 56

Question 11.
If the sum 1 + 2 + 22 + ………. + 2n-1 is 255, find the value of n.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 57

Question 12.
Find the geometric mean between :
(i) \(\frac{4}{9} \text { and } \frac{9}{4}\)
(ii) 14 and \(\frac{7}{32}\)
(iii) 2a and 8a3
Solution 12(i).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 59

Solution 12(ii).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 58

Solution 12(iii).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 60

Question 13.
The sum of three numbers in G.P. is \(\frac{39}{10}\) and their product is 1. Find the numbers.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 61

Question 14.
The first term of a G.P. is -3 and the square of the second term is equal to its 4th term. Find its 7th term.
Solution:

Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 62

Question 15.
Find the 5th term of the G.P. \(\frac{5}{2}\), 1, …..
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 63

Question 16.
The first two terms of a G.P. are 125 and 25 respectively. Find the 5th and the 6th terms of the G.P.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 64

Question 17.
Find the sum of the sequence –\(\frac{1}{3}\), 1, – 3, 9, …………. upto 8 terms.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 65

Question 18.
The first term of a G.P. in 27. If the 8thterm be \(\frac{1}{81}\), what will be the sum of 10 terms ?
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 66

Question 19.
Find a G.P. for which the sum of first two terms is -4 and the fifth term is 4 times the third term.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 67

Additional Questions

Question 1.
Find the sum of n terms of the series :
(i) 4 + 44 + 444 + ………
(ii) 0.8 + 0.88 + 0.888 + …………..
Solution 1(i).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 68

Solution 1(ii).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 69

Question 2.
Find the sum of infinite terms of each of the following geometric progression:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 70
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 71
Solution 2(i).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 72

Solution 2(ii).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 73

Solution 2(iii).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 74

Solution 2(iv).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 75

Solution 2(v).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 76

Question 3.
The second term of a G.P. is 9 and sum of its infinite terms is 48. Find its first three terms.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 77

Question 4.
Find three geometric means between \(\frac{1}{3}\) and 432.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 78

Question 5.
Find :
(i) two geometric means between 2 and 16
(ii) four geometric means between 3 and 96.
(iii) five geometric means between \(3 \frac{5}{9}\) and \(40 \frac{1}{2}\)
Solution 5(i).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 79

Solution 5(ii).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 80.

Solution 5(iii).
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 81

Question 6.
The sum of three numbers in G.P. is \(\frac{39}{10}\) and their product is 1. Find the numbers.
Solution:
Sum of three numbers in G.P. = \(\frac{39}{10}\) and their product = 1
Let number be \(\frac{a}{r}\), a, ar, then
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 82
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 86

Question 7.
Find the numbers in G.P. whose sum is 52 and the sum of whose product in pairs is 624.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 84

Question 8.
The sum of three numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Geometric Progression - 85

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