nth Term of GP

Q. If $3^{rd}$ term of a G.P is 12 and $6^{th}$ term is 96, then its $7^{th}$ term is .

1. 288
2. 192
3. 182
4. 144

Q. Three positive numbers form an increasing GP. If the middle term in this GP is doubled then new numbers are in AP, find the common ratio of the GP. Again, if the middle term in the GP tripled, then check whether the common ratio of the GP will be same or not.

Or

Find the first term and common ratio of an infinite geometric series, if its sum is 4 and the second term is $\frac{3}{4}$.

Q.

If a, b, c are in GP, Which of the following will be the common ratio of the GP.

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. 

2. 

3. 

4. 1

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 the first term of a G.P. $a_1$, $a_2$, $a_3$, .........is unity such that

4$a_2$ + 5$a_3$ is least, then the common ratio of G.P. is

1. 

2. 

3. 

4. None of these

Q. Prove the following by using the principle of mathematical induction for all $n\in N:1.3+2.3^2+3.3^3+.....+n.3{}^n=\frac{(2n-1)3^{n+1}+3}{4}$

Q.

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

1. 144

2. 288

3. 192

4. 182

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.

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