CBSE - Class 11 Mathematics Sequences and Series Worksheet
EXERCISE 8.2
1.
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.
2.
Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.
3.
How many terms of G.P. $3, 3^2, 3^3, ...$ are needed to give the sum 120?
4.
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.
5.
The 4th term of a G.P. is square of its second term, and the first term is -3. Determine its 7th term.
6.
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 $P^2 = (ab)^n$.
7.
For what values of $x$, the numbers $-\frac{2}{7}, x, -\frac{7}{2}$ are in G.P.?
8.
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 $\frac{1}{r^n}$.
9.
If $a, b, c$ and $d$ are in G.P. show that $(a^2 + b^2 + c^2) (b^2 + c^2 + d^2) = (ab + bc + cd)^2$.
10.
Which term of the following sequence: (c) $\frac{1}{3}, \frac{1}{9}, \frac{1}{27}, ...$ is $\frac{1}{19683}$?
11.
Insert two numbers between 3 and 81 so that the resulting sequence is G.P.
12.
Find the 20th and nth terms of the G.P. $\frac{5}{2}, \frac{5}{4}, \frac{5}{8}, ...$
13.
Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2, $\frac{1}{2}$.
14.
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.
15.
Find the sum to indicated number of terms in the geometric progression: $x^3, x^5, x^7, ...$ $n$ terms (if $x \ne \pm 1$).
16.
Which term of the following sequence: (b) $\sqrt{3}, 3, 3\sqrt{3}, ...$ is 729?
17.
If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.
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.
Which term of the following sequence: (a) $2, 2\sqrt{2}, 4, ...$ is 128?
20.
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.
