Nth Term of GP

Q.

The pth, qth and rth terms of an A.P. are a, b, c, respectively. Show that $(q-r)a+(r-p)b+(p-q)c=0$.

Q. The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2 nd hour, 4 th hour and n th hour?

Q. In an increasing geometric series, the sum of the second and the sixth term is $\frac{25}{2}$ and the product of the third and fifth term is $25.$ Then, the sum of $4^{\text{th}},6^{\text{th}}$ and $8^{\text{th}}$ terms is equal to :

1. $35$
2. $30$
3. $26$
4. $32$

Q. 2.If the 6th term of a GP be 2, then the product of its first 11 term will be?

Q. Find four numbers forming a geometric progression in which third term is greater than the first term by 9, and the second term is greater than the 4 th by 18.

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. 2

2. 3

3. 4

4. 1

Q. The 5 th , 8 th and 11 th terms of a G.P. are p , q and s , respectively. Show that q 2 = ps .

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. Let $a_1,a_2,\dots ,a_{10}$ be a G.P. If $\frac{a_3}{a_1}=25$, then $\frac{a_9}{a_5}$ equals:

1. $2(5{)}^2$
2. $4\left(5^2\right)$
3. $5^3$
4. $5^4$

Q. If the 4 th , 10 th and 16 th terms of a G.P. are x, y and z , respectively. Prove that x , y , z are in G.P.

Q. Which term of the following sequences:(a) 2, 2 2, 4.. is 128?5.(b) 3, 3, 33...is729?'is3 9 27'19683

Q. The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.

Q. Find the 20 th and n th terms of the G.P.

Q. The number of bacteria in a certain culture doubles every hour. If there were $30$ bacteria present in the culture originally, how many bacteria will be present at the end of $2^{nd}$ hour $4^{th}$ hour and $n^{th}$ hour?

Q. The 4 th term of a G.P. is square of its second term, and the first term is –3. Determine its 7 th term.

Q. If 3rd, 7th, 12th terms of an ap are 3 consecutive terms of a gp then common ratio is

Q. Let $t_n$ represents the $n^{th}$ term of a G.P. If $t_3=2$ and $t_6=-\frac{1}{4},$ then the value of $t_{10}$ is

1. $-\frac{1}{128}$
2. $-\frac{1}{64}$
3. $\frac{1}{128}$
4. $\frac{1}{64}$

Q. The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.

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

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

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

Q. Find:
(i) the ninth term of the G.P. 1, 4, 16, 64, ...

(ii) the 10th term of the G.P. $-\frac{3}{4},\frac{1}{2},-\frac{1}{3},\frac{2}{9},...$

(iii) the 8th term of the G.P. 0.3, 0.06, 0.012, ...

(iv) the 12th term of the G.P. $\frac{1}{a^3{x}^3},ax,a^5{x}^5,...$

(v) nth term of the G.P. $\sqrt{3},\frac{1}{\sqrt{3}},\frac{1}{3\sqrt{3}},...$

(vi) the 10th term of the G.P. $\sqrt{2},\frac{1}{\sqrt{2}},\frac{1}{2\sqrt{2}},...$

Q. The sum of first four terms of a geometric progression (G.P.) is $\frac{65}{12}$ and the sum of their respective reciprocals is $\frac{65}{18}.$ If the product of first three terms of the G.P. is $1,$ and the third term is $\alpha ,$ then $2\alpha$ is

Q. The first term of a GP is -3 and the square of the second term is equal to its4th term. Find its 7th term.