## Kerala Plus One Maths Chapter Wise Previous Questions and Answers Chapter 9 Sequences and Series

Question 1.

Find the sum to n terms of the sequence 4 + 44 + 444 + [March-2018]

Answer:

Question 2.

a. Find the n^{th} term of the sequence 3,5,7 ………….

b. Find the sum to n terms of the series.

3 × 1^{2} + 5 ×2^{2} + 7 ×3^{2}+… [March-2018]

Answer:

a.t_{n}= 3+(n-1)2 = 2n+1

Let T_{n} denotes the nth term of the given series.

T_{n} = (n^{th} term of 3, 5, 7, ….)(n^{th} term of 1^{2}, 2^{2}, 3^{2}……… )

Question 3.

a The sum of the infinite series

1, …………………. is ………………..

i.

ii.

iii.

iv.

b. Find the sum of all natural numbers lying between 100 and 1000 which are multiples of 5.

c. Find the sum to n terms of the sequence 8,88,888,………….

**OR**

a The 6^{th} term of the GP

i.

ii.

iii.

iv.

b. Find the sum to n terms of the series 3×1^{2}+5×2^{2}+7×3^{2} +………..[March – 2017]

Answer:

Question 4.

The n^{th} term of the G.P. 5, 25, 125,……… is….

i. n^{5}

ii. 5^{n }iii. (2n)^{5}

iv. 5^{2n }b. Find the sum of all natural numbers between 200 and 1000 which are multiples of 10.

c. Calculate the sum of n-terms of the series whose n^{th} term is a_{n} = n(n+3). [March-2016]

Answer:

Question 5.

a. The 3^{rd} term of the sequence whose n^{th }terms is is……….

i.

ii.

iii.

iv.

b. Insert three numbers between 1 and 256 so that the resulting sequence is a GP.

c. If m^{th} term of an A.P. is n and n^{th} term is m, where m ≠ n, find p^{th} term.

**OR **a. The 6

^{th}term of the sequence whose n

^{th }term is

i. 3

ii.

iii.

iv.

b. Find the sum of infinity of the sequence 1,

………………

c. If a, b, c are in AP and a

^{1/x}=b

^{1/y}= c

^{1/z}, prove that x, y, z are in AP. [March-2015]

Answer:

.

Question 6.

a Find the 5^{th} term of the sequence whose n^{th} term is

b. Write the sum of the first ‘n’ natural numbers,

c. The 5^{th}, 8^{th} and 11^{th} terms of a GP. are p, q, and s respectively. Prove that q^{2 }=ps [March-2014]

Answer:

Question 7.

Find the 5^{th} term of the sequence whose n^{th }term,

b. Find 7+ 77 + 111 + 7777 + ……………… to n terms.

c. Find the sum to n terms of the series 1 × 2 + 2×3 + 3×4 + 4×5 +…………… [March-2013]

Answer:

Question 8.

i. If the p^{th}, q^{th} and r^{th} terms of a GP are a, b and c respectively, prove that

a^{q-r }b^{r-p }c^{p-q }=1

If AM and GM of two number are 10 and 8 respectively, find the numbers. [February-2013]

Answer:

Question 9.

a. Find the 10 term of an A.P. Whose n^{th }terms is

b. Find the sum of the first 10 terms of the above A. P

c. Find the sum first 10 terms of a GP. whose 3^{rd} term is 12 and 8^{th} term is 384. [March-2012]

Answer:

Question 10.

i. Which of the following is the nth term of an A.P?

a. 3 – 2 n

b. n^{2}– 3

c. 3^{n}-2

d. 2 – 3n^{2}

ii. Find the 10th term of the sequence -6,,-5……….

iii. The sum of the first three terms of a GP is and their product is 1. Find the common ratio and the terms. [March-2011]

Answer:

Question 11.

i. In an AP, the first term is 2 and the sum of the first five terms is one fourth the sum of the next five terms.

a. Find the common difference.

b. Find the 20^{th }c. If AM and GM of two numbers are 10 and 8 respectively, find the numbers. [March-2010]

Answer:

Question 12.

a. In an AP if m^{th} term is ‘n’ and n^{th} term is ‘m’, m≠n, find the (m + n)^{th} term.

b. If 3^{rd}, 8^{th} and 13^{th} terms of GP are x, y, z respectively, prove that x, y, z are in GP.

c. Prove that x, y, z in the above satisfies the equation [September – 2010]

Answer:

Question 13.

i. If the n^{th} term of a sequence is then find its first two terms.

ii. How many terms of A.P-6, -11/2, -5, …. are needed to give the sum -25?

iii. Find the 10″^{1} term of a GP whose 3^{rd} term is 24 and 6^{th} term is 192. [August-2009]

Answer:

Question 14.

a. Find the value of x in which the numbers -2/7, x, -7/2 are in GP.

b. Find the sum of all natural numbers between 100 and 1000 which are multiple of 5.

c. Prove that 1^{2} + 2^{2} + 3^{2} +………. + n^{2}=

[March – 2009]

Ans:

Question 15.

Find the sum of the sequence to n terms 9,99,999……… [September-2008]

Answer:

S =9+ 99 + 999 + ….to n terms

Question 16.

If a_{1}= 1, a_{n} = a_{n-1} +2, for n≥2 then write the 4 terms of the sequence. [February-2008]

Answer:

Question 17.

The sum of 3 terms of a GP is 39/10 and their product is 1. Find the first term, common ratio, and the terms. [February-2008]

Answer:

Question 18.

State whether the following is true or false. “If each term of an A.P is multiplied by a constant then the resulting sequence is also an A.P. [February-2008]

Answer:

True. If a non-zero constant is added or subtracted or multiplied or divided to each term of an A.P, then the resulting sequence is also an A.P.

Question 19.

a. The n^{th} term of a sequence is a_{n} = 1 – 2n

(i) a_{1}-a_{2} =……………….

(ii) Find a_{n+1} – a_{n }(iii) Does the above sequence form an A.P? Justify your answer.

b. The n^{th} term of a sequence is given by n^{2} + 3. Will it be an A.P? Give reason. [March-2007]

Answer:

Question 20.

Find the sum to n terms of 4 + 44 + 444 + …….. [June-2007]

Answer:

Question 21.

Show that the sum of (m + n)^{th} and (m – n)^{th }terms of an A.P is equal to the twice of the m^{th }terms.

Answer: