Nth Term of GP

Q. Given log₁₀ a = m and log₁₀ b = n, express a³/b² in terms of m and n.

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 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.

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.

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.

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

Q. If x, y, z are $pth$ , $qth$ and $rth$ terms respectively, of an A.P. and also of G.P., then $x^{y-z}{y}^{z-x}{z}^{x-y}$, is equal to

1. $xyz$
2. $0$
3. $1$
4. $noneofthese$

Q. Insert three numbers $1$ and $256$ so that the resulting sequence is a G.P.

1. $0,16,64$
2. $4,6,64$
3. $4,0,64$
4. $4,16,64$