CBSE - Class 11 Mathematics Sequences and Series Worksheet
1.
How many terms of G.P. $3, 3^2, 3^3, ...$ are needed to give the sum 120?
2.
Find the indicated term in the sequence whose nth term is: $a_n = (-1)^{n-1}n^3; a_9$
3.
If the 4th, 10th and 16th terms of a G.P. are $x, y$ and $z$, respectively. Prove that $x, y, z$ are in G.P.
4.
Write the first five terms of the sequence and obtain the corresponding series: $a_1 = 3, a_n = 3a_{n-1} + 2$ for all $n > 1$
5.
The 5th, 8th and 11th terms of a G.P. are $p, q$ and $s$, respectively. Show that $q^2 = ps$.
6.
150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day, 4 more workers dropped out on third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was completed.
7.
Given a G.P. with $a = 729$ and 7th term 64, determine $S_7$.
8.
What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?
9.
Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.
10.
Write the first five terms of the sequence and obtain the corresponding series: $a_1 = -1, a_n = \frac{a_{n-1}}{n}, n \ge 2$
11.
A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.
12.
Write the first five terms of the sequence and obtain the corresponding series: $a_1 = a_2 = 2, a_n = a_{n-1} - 1, n > 2$
13.
Find four numbers forming a geometric progression in which the third term is greater than the first term by 9, and the second term is greater than the 4th by 18.
14.
The ratio of the A.M. and G.M. of two positive numbers $a$ and $b$, is $m : n$. Show that $a : b = (m + \sqrt{m^2-n^2}) : (m - \sqrt{m^2-n^2})$.
15.
If $\frac{a+bx}{a-bx} = \frac{b+cx}{b-cx} = \frac{c+dx}{c-dx} (x \ne 0)$, then show that $a, b, c$ and $d$ are in G.P.
16.
The 4th term of a G.P. is square of its second term, and the first term is -3. Determine its 7th term.
17.
Write the first five terms of the sequence whose nth term is: $a_n = 2^n$
18.
If the $p^{th}, q^{th}$ and $r^{th}$ terms of a G.P. are $a, b$ and $c$, respectively. Prove that $a^{q-r} b^{r-p} c^{p-q} = 1$.
19.
The Fibonacci sequence is defined by $1 = a_1 = a_2$ and $a_n = a_{n-1} + a_{n-2}, n > 2$. Find $\frac{a_{n+1}}{a_n}$, for $n = 1, 2, 3, 4, 5$
20.
The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.
