CBSE - Class 11 Mathematics Sequences and Series Worksheet
1.
The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.
2.
The sum of first three terms of a G.P. is $\frac{39}{10}$ and their product is 1. Find the common ratio and the terms.
3.
Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.
4.
How many terms of G.P. $3, 3^2, 3^3, ...$ are needed to give the sum 120?
5.
Write the first five terms of the sequence whose nth term is: $a_n = (-1)^{n-1} 5^{n+1}$
6.
Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?
7.
The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to $n$ terms of the G.P.
8.
The 4th term of a G.P. is square of its second term, and the first term is -3. Determine its 7th term.
9.
Write the first five terms of the sequence whose nth term is: $a_n = n \frac{n^2 + 5}{4}$
10.
The ratio of the A.M. and G.M. of two positive numbers $a$ and $b$, is $m : n$. Show that $a : b = (m + \sqrt{m^2-n^2}) : (m - \sqrt{m^2-n^2})$.
11.
If the first and the $n^{th}$ term of a G.P. are $a$ and $b$, respectively, and if $P$ is the product of $n$ terms, prove that $P^2 = (ab)^n$.
12.
Write the first five terms of the sequence whose nth term is: $a_n = 2^n$
13.
For what values of $x$, the numbers $-\frac{2}{7}, x, -\frac{7}{2}$ are in G.P.?
14.
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 $\frac{1}{r^n}$.
15.
If $a$ and $b$ are the roots of $x^2 - 3x + p = 0$ and $c, d$ are roots of $x^2 - 12x + q = 0$, where $a, b, c, d$ form a G.P. Prove that $(q + p) : (q - p) = 17:15$.
16.
If $a, b, c$ and $d$ are in G.P. show that $(a^2 + b^2 + c^2) (b^2 + c^2 + d^2) = (ab + bc + cd)^2$.
17.
Write the first five terms of the sequence whose nth term is: $a_n = \frac{2n - 3}{6}$
18.
If $a, b, c, d$ are in G.P, prove that $(a^n + b^n), (b^n + c^n), (c^n + d^n)$ are in G.P.
19.
Which term of the following sequence: (c) $\frac{1}{3}, \frac{1}{9}, \frac{1}{27}, ...$ is $\frac{1}{19683}$?
20.
Insert two numbers between 3 and 81 so that the resulting sequence is G.P.
