CBSE - Class 11 Mathematics Sequences and Series Worksheet
1.
Find the sum to indicated number of terms in the geometric progression: $x^3, x^5, x^7, ...$ $n$ terms (if $x \ne \pm 1$).
2.
A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when 8th set of letter is mailed.
3.
Write the first five terms of the sequence whose nth term is: $a_n = (-1)^{n-1} 5^{n+1}$
4.
Find the indicated term in the sequence whose nth term is: $a_n = (-1)^{n-1}n^3; a_9$
5.
If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are $A \pm \sqrt{(A+G)(A-G)}$.
6.
If $a, b, c$ and $d$ are in G.P. show that $(a^2 + b^2 + c^2) (b^2 + c^2 + d^2) = (ab + bc + cd)^2$.
7.
If $f$ is a function satisfying $f(x+y) = f(x)f(y)$ for all $x, y \in N$ such that $f(1) = 3$ and $\sum_{x=1}^{n} f(x) = 120$, find the value of $n$.
8.
Find the sum to indicated number of terms in the geometric progression: $1, -a, a^2, -a^3, ...$ $n$ terms (if $a \ne -1$).
9.
Write the first five terms of the sequence and obtain the corresponding series: $a_1 = -1, a_n = \frac{a_{n-1}}{n}, n \ge 2$
10.
Evaluate $\sum_{k=1}^{11} (2 + 3^k)$.
11.
Write the first five terms of the sequence and obtain the corresponding series: $a_1 = a_2 = 2, a_n = a_{n-1} - 1, n > 2$
12.
The 5th, 8th and 11th terms of a G.P. are $p, q$ and $s$, respectively. Show that $q^2 = ps$.
13.
Insert two numbers between 3 and 81 so that the resulting sequence is G.P.
14.
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.
15.
Which term of the following sequence: (a) $2, 2\sqrt{2}, 4, ...$ is 128?
16.
What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?
17.
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 $n = 1, 2, 3, 4, 5$
18.
The 4th term of a G.P. is square of its second term, and the first term is -3. Determine its 7th term.
19.
Show that the ratio of the sum of first $n$ terms of a G.P. to the sum of terms from $(n + 1)^{th}$ to $(2n)^{th}$ term is $\frac{1}{r^n}$.
20.
Show that the products of the corresponding terms of the sequences $a, ar, ar^2, ...ar^{n-1}$ and $A, AR, AR^2, ... AR^{n-1}$ form a G.P, and find the common ratio.
