CBSE - Class 11 Mathematics Sequences and Series Worksheet
1.
A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much will the tractor cost him?
2.
Write the first five terms of the sequence whose nth term is: $a_n = 2^n$
3.
If $a, b, c$ and $d$ are in G.P. show that $(a^2 + b^2 + c^2) (b^2 + c^2 + d^2) = (ab + bc + cd)^2$.
4.
Find the 20th term of the series $2 \times 4 + 4 \times 6 + 6 \times 8 + ... + n$ terms.
5.
Find the sum to indicated number of terms in the geometric progression: $1, -a, a^2, -a^3, ...$ $n$ terms (if $a \ne -1$).
6.
Write the first five terms of the sequence whose nth term is: $a_n = \frac{2n - 3}{6}$
7.
Find the indicated term in the sequence whose nth term is: $a_n = \frac{n(n-2)}{n+3}; a_{20}$
8.
Find the sum of the following series up to $n$ terms: (ii) $.6 + .66 + .666 + ...$
9.
Which term of the following sequence: (b) $\sqrt{3}, 3, 3\sqrt{3}, ...$ is 729?
10.
Write the first five terms of the sequence whose nth term is: $a_n = n \frac{n^2 + 5}{4}$
11.
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?
12.
Which term of the following sequence: (a) $2, 2\sqrt{2}, 4, ...$ is 128?
13.
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 $P^2 = (ab)^n$.
14.
Find the sum of the following series up to $n$ terms: (i) $5 + 55 + 555 + ...$
15.
Find the sum to indicated number of terms in the geometric progression: 0.15, 0.015, 0.0015, ... 20 terms.
16.
Write the first five terms of the sequence whose nth term is: $a_n = (-1)^{n-1} 5^{n+1}$
17.
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 $(q + p) : (q - p) = 17:15$.
18.
Find the sum to $n$ terms of the sequence, 8, 88, 888, 8888... .
19.
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.
20.
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.
