nth Term of G.P

Q.

In a geometric progression, the ratio of the sum of the first three terms and the first six terms is $125:152$. The common ratio.

1. $\frac{1}{5}$

2. $\frac{2}{5}$

3. $\frac{4}{5}$

4. $\frac{3}{5}$

Q. If $a_1$, $a_2$, $a_3$($a_1>0)$ are three successive terms of a G.P. with common ratio r, then find the value of r for which $a_3>4a_2-3a_1$.

Q.

In a G.P., 3rd term is 16 and the 6th term is 128. Find the 10th term.

1. $a_{10}=512$

2. $a_{10}=1048$

3. $a_{10}=2048$

4. $a_{10}=256$

Q.

If 3rd term of a G.P is 12 and 6th term is 96, find its 7th term.

1. 182

2. 288

3. 144

4. 192

Q.

$7^{th}$ term of the sequence $\sqrt{2},\sqrt{10},5\sqrt{2},.........$ is

1. $125\sqrt{2}$

2. $125\sqrt{10}$

3. $25\sqrt{2}$

4. 125

Q.

Find the sum of the geometric progressions $1,-a,a²,-a^3,...n\text{terms}\left(ifa\ne -1\right)$

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 $(p+q{)}^{th}$ 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. $\sqrt{mn}$

4. $(m-n)$

Q.

Find $a_{20}$ of a geometric sequence, if the first few terms of the sequence are given by $-\frac{1}{2},\frac{1}{4},-\frac{1}{8},\frac{1}{16},\cdots$

1. ${20}^{20}$

2. $\frac{1}{2^{20}}$

3. $\frac{1}{20}$

4. $\frac{1}{2^{19}}$

Q. If a, b and c are in G.P., then $\frac{b-a}{b-c}+\frac{b+a}{b+c}=$

1. $b^2$$c^2$
2. $0$
3. $ab$
4. $ac$

Q. The 8th term of G.P. 5, 10, 20, ... is 540.

1. False
2. True

Q.

If the $4^{th}$, $7^{th}$ and ${10}^{th}$ terms of a G.P. be a, b, c respectively, then the relation between a, b, c is

1. b = $\frac{a+c}{2}$

2. $a^2$ = bc

3. $b^2$ = ac

4. $c^2$ = ab

Q. Find $a_{20}$ of a geometric sequence, if the first few terms of the sequence are given by $-\frac{1}{2},\frac{1}{4},-\frac{1}{8},\frac{1}{16},\cdots$

Q.

Find the $4^{\mathrm{th}}$ term from the end of the GP: $\frac{2}{27},\frac{2}{9},\frac{2}{3},\dots ,162$

Q. Find a Geometric Progression for which the sum of first two terms is -4 and the fifth term is 4 times the third term.
(2 marks)

Q. If $a_1$, $a_2$, $a_3$($a_1>0)$ are three successive terms of a G.P. with common ratio r, then find the value of r for which $a_3>4a_2-3a_1$.

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

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

Q. The ratio of any two consecutive terms in a G.P is called common ratio of the GP.

1. False
2. True

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, 120, 240, ...

2. 60, 240, 960...

3. 60, 300, 1800, ...

4. 60, 180, 540...

Q.

Find $a_{20}$ of a geometric sequence, if the first few terms of the sequence are given by $-\frac{1}{2},\frac{1}{4},-\frac{1}{8},\frac{1}{16},\cdots$

1. ${20}^{20}$

2. $\frac{1}{2^{20}}$

3. $\frac{1}{20}$

4. $\frac{1}{2^{19}}$

Q. $2^2,2^3,2^4...$
The next term in this series is $2^5$.

1. False
2. True