Nth term of GP

Q.

Find the maximum profit that a company can make if the profit function is given by $p\left(x\right)=41-72x-18x^2$.

Q. The seventh term of a G.P. is 27 times the fourth term and the fifth term is 243. The third term of this G.P. is .

1. 9
2. 81
3. 27
4. 36

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

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

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

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. $\frac{m}{n}$

2. $\sqrt{mn}$

3. o

4. mn

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

1. 192

2. 288

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. $\frac{3}{4}$

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

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

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

Q. The 6th term from the end of the sequence 4, 8, 16, 32, ....., 16384 is .

1. 1024
2. 512
3. 256
4. 64

Q. The nth term of a GP 18, -12, 8, ...... is $\frac{512}{729}$. The value of n is .

1. 7
2. 8
3. 9
4. 10