Kerala Plus One Maths Chapter Wise Previous Questions and Answers Chapter 9 Sequences and Series
Find the sum to n terms of the sequence 4 + 44 + 444 + [March-2018]
a. Find the nth term of the sequence 3,5,7 ………….
b. Find the sum to n terms of the series.
3 × 12 + 5 ×22 + 7 ×32+… [March-2018]
a.tn= 3+(n-1)2 = 2n+1
Let Tn denotes the nth term of the given series.
Tn = (nth term of 3, 5, 7, ….)(nth term of 12, 22, 32……… )
a The sum of the infinite series
1, …………………. is ………………..
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,………….
a The 6th term of the GP
b. Find the sum to n terms of the series 3×12+5×22+7×32 +………..[March – 2017]
The nth term of the G.P. 5, 25, 125,……… is….
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 nth term is an = n(n+3). [March-2016]
a. The 3rd term of the sequence whose nth terms is is……….
b. Insert three numbers between 1 and 256 so that the resulting sequence is a GP.
c. If mth term of an A.P. is n and nth term is m, where m ≠ n, find pth term.
a. The 6th term of the sequence whose nth term is
b. Find the sum of infinity of the sequence 1,
c. If a, b, c are in AP and a1/x=b1/y = c1/z, prove that x, y, z are in AP. [March-2015]
a Find the 5th term of the sequence whose nth term is
b. Write the sum of the first ‘n’ natural numbers,
c. The 5th, 8th and 11th terms of a GP. are p, q, and s respectively. Prove that q2 =ps [March-2014]
Find the 5th term of the sequence whose nth 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]
i. If the pth, qth and rth terms of a GP are a, b and c respectively, prove that
aq-r br-p cp-q =1
If AM and GM of two number are 10 and 8 respectively, find the numbers. [February-2013]
a. Find the 10 term of an A.P. Whose nth 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 3rd term is 12 and 8th term is 384. [March-2012]
i. Which of the following is the nth term of an A.P?
a. 3 – 2 n
b. n2– 3
d. 2 – 3n2
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]
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 20th
c. If AM and GM of two numbers are 10 and 8 respectively, find the numbers. [March-2010]
a. In an AP if mth term is ‘n’ and nth term is ‘m’, m≠n, find the (m + n)th term.
b. If 3rd, 8th and 13th 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]
i. If the nth 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 3rd term is 24 and 6th term is 192. [August-2009]
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 12 + 22 + 32 +………. + n2=
[March – 2009]
Find the sum of the sequence to n terms 9,99,999……… [September-2008]
S =9+ 99 + 999 + ….to n terms
If a1= 1, an = an-1 +2, for n≥2 then write the 4 terms of the sequence. [February-2008]
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]
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]
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.
a. The nth term of a sequence is an = 1 – 2n
(i) a1-a2 =……………….
(ii) Find an+1 – an
(iii) Does the above sequence form an A.P? Justify your answer.
b. The nth term of a sequence is given by n2 + 3. Will it be an A.P? Give reason. [March-2007]
Find the sum to n terms of 4 + 44 + 444 + …….. [June-2007]
Show that the sum of (m + n)th and (m – n)th terms of an A.P is equal to the twice of the mth terms.