Nth Term of GP

Q.

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

1. 1

2. 

3. 

4. 

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

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

Q.

The number which should be added to the number added to the numbers 2, 14, 62 so that the resulting numbers may be in G.P. is

1. 1

2. 2

3. 3

4. 4

Q.

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

1. 288

2. 192

3. 182

4. 144

Q.

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

1. o

2. mn

3. $\frac{m}{n}$

4. $\sqrt{mn}$

Q.

If the $5^{th}$ term of a G.P. containing positive terms is $\frac{1}{3}$ and $9^{th}$ term is $\frac{16}{243}$, then the $4^{th}$ term will be

1. 

2. 

3. 

4. 

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 ___.

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

Q.

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

1. mn

2. o

3. $\frac{m}{n}$

4. $\sqrt{mn}$

Q.

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

1. 192

2. 182

3. 144

4. 288

Q.

If the $5^{th}$ term of a G.P. containing positive terms is $\frac{1}{3}$ and $9^{th}$ term is $\frac{16}{243}$, then the $4^{th}$ term will be

1. 

2. 

3. 

4.