General Term of a GP

Q. $8^{\text{th}}$ term of the GP 1, 3, 9, .... = ______

1. 2187
2. 729
3. 6561
4. 2041

Q. The $7^{\text{th}}$ term of the GP $2,-6,18,...$ is .

1. 1458
2. 1458
3. 4374
4. -4374

Q. Three positive numbers form an increasing GP. If the middle term of the GP is doubled, then new numbers are in AP. Then, the common ratio of the GP is
(IIT JEE Main 2014)

1. $\sqrt{2}+\sqrt{3}$
2. $3+\sqrt{2}$
3. $2-\sqrt{3}$
4. $2+\sqrt{3}$

Q.

Which term of the GP 1, 2, 4, 8, .... is 512?

1. 8

2. 9

3. 10

4. 11

Q.

The product of $2^{\text{nd}}$ term and $4^{\text{th}}$ term of a G.P is 57600. If its $1^{st}$ term is 60, then find the G.P..

1. 60, 180, 540...

2. 60, 240, 960...

3. 60, 120, 240, ...

4. 60, 300, 1800, ...

Q.

The terms of a G.P. are positive. If each term is equal to the sum of two terms that follow it, then the common ratio is ___.

1. $\frac{\sqrt{5}-1}{2}$

2. $\frac{-1-\sqrt{5}}{2}$

3. 1

4. $2\sqrt{5}$

Q.

If a, b, c are $p^{th}$, $q^{th}$, and $m^{th}$ terms of a G.P., then $\left(\frac{c}{b}{)}^p\right(\frac{b}{a}{)}^m(\frac{a}{c}{)}^q$ is equal to

1. 1

2. $a^p{b}^q{c}^r$

3. $a^q{b}^r{c}^p$

4. $a^r{b}^p{c}^q$

Q. $\sqrt{3},\frac{1}{\left(\sqrt{3}\right)},\frac{1}{3\left(\sqrt{3}\right)}.....$
The ${19}^{\text{th}}$ term of the above sequence is .

Q.

Fourth term of a G.P is 3 and the product of the $3^{\text{rd}}$ and $8^{\text{th}}$ term is 243. Find its $7^{\text{th}}$ term.

1. 81

2. 83

3. 27

4. 243

Q. $\sqrt{3},\frac{1}{\left(\sqrt{3}\right)},\frac{1}{3\left(\sqrt{3}\right)}.....$
The ${19}^{\text{th}}$ term of the above sequence is .

1. $\frac{\sqrt{3}}{3^{18}}$
2. $\frac{3^{15}}{2}$
3. $\frac{\sqrt{3^7}}{3^{26}}$

Q.

Find the number of terms in the G.P 6, 12, 24 ... 1536.

1. 8

2. 10

3. 9

4. 6

Q.

If the $3^{\text{rd}}$ and $6^{\text{th}}$ terms of a G.P are 12 and 96, then its common ratio is ___.

1. 4

2. 9

3. 2

4. 7

Q.

If the first term of a G.P. is 5 and the common ratio is -5, then 3125 is the ____ term.

1. $6^{th}$

2. $5^{th}$

3. $7^{th}$

4. $8^{th}$

Q.

If the $(p+q{)}^{th}$ term of a G.P. is m and $(p-q{)}^{th}$ term is n, then pth term will be _____.

1. $\left(\frac{m}{n}\right)$

2. $mn$

3. $(m-n)$

4. $\sqrt{mn}$

Q. $\sqrt{3},\frac{1}{\left(\sqrt{3}\right)},\frac{1}{3\left(\sqrt{3}\right)}.....$
The ${19}^{\text{th}}$ term of the above sequence is .

1. $\frac{\sqrt{3}}{3^{18}}$
2. $\frac{3^{15}}{2}$
3. $\frac{\sqrt{3^7}}{3^{26}}$

Q. If $S$ is the sum to infinity of a GP, whose first term is $a$, then the sum of the first $n$ terms is

1. $S{(1-\frac{a}{S})}^n$
2. $a[1-{(1-\frac{a}{S})}^n]$
3. none of these
4. $S[1-{(1-\frac{a}{S})}^n]$

Q. Match each of the following GPs with the correct next terms.

1. 32
2. 8
3. 81
4. $x^{4}y$

Q. For first $n$ natural numbers we have the following results with usual notations $\sum _{r=1}^{n}r=\frac{n(n+1)}{2},\sum _{r=1}^n{r}^2=\frac{n(n+1)(2n+1)}{6},\sum _{r=1}^n{r}^3={\left(\sum _{r=1}^{n}r\right)}^2$ If $a_1{a}_2....a_n\in A.P$ then sum to $n$ terms of the sequence $\frac{1}{a_1{a}_2},\frac{1}{a_2{a}_3},...\frac{1}{a_{n-1}{a}_n}$ is equal to $\frac{n-1}{a_1{a}_n}$
and the sum to $n$ terms of a $G.P$ with first term '$a$' & common ratio '$r$' is given by $S_n=\frac{lr-a}{r-1}$ for $r\ne 1$ for $r=1$ sum to $n$ terms of same $G.P.$ is $n$ $a$, where the sum to infinite terms of$G.P.$ is the limiting value of
$\frac{lr-a}{r-1}$ when $n\to \infty ,\left|r\right|<l$ where $l$ is the last term of $G.P.$ On the basis of above data answer the following questionsThe sum to infinite terms of the series $\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+..$ is equal to ?

1. $\frac{4}{3}$
2. $\frac{3}{4}$
3. $\frac{8}{3}$
4. Does not exit

Q.

Which term of the GP 1, 2, 4, 8, .... is 512?

1. 8

2. 9

3. 10

4. 11