Nth Term of GP

Q.

In a GP the 3rd term is 24 and the 6th term is 192. Find the 10th term.

Q.

Which term of the progression 18, - 12, 8, .... is $\frac{512}{729}$ ?

Q.

What is $n^{th}$ term?

Q.

Which term of the progression 0.004, 0.02, 0.1, .... is 12.5 ?

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.

Find the 20^th and n^thterms of the G.P.

Q.

If the G.P.'s 5, 10, 20, ...... and 1280, 640, 320, .... have their nth terms equal, find the value of n.

Q.

Three numbers are in G.P. such that their sum is $38$ and their product is $1728$.

The greatest number among them is

1. $18$

2. $16$

3. $14$

4. None of these

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.

The 4th term of a G.P. is square of its second term, and the first term is - 3. Find its 7th term.

Q. In an increasing geometric progression, the sum of the first term and the last term is $66$, the product of the second terms from the beginning and the end is $128$ and sum of all terms is $126$. Then the number of terms in the progression is

1. $5$
2. $6$
3. $7$
4. $8$

Q.

In a G.P. if the $(m+n{)}^{th}$ term is p and $(m-n{)}^{th}$ term is q, then its $m^{th}$ term is

1. 0

2. $\sqrt{pq}$

3. $\frac{1}{2}(p+q)$

4. pq

Q.

If pth, qth and rth terms of an A.P. are in G.P., then the common ratio of this G.P. is

1. $\frac{p-q}{q-r}$

2. $\frac{q-r}{p-q}$

3. pqr

4. none of these

Q.

The nth term of a G.P. is 128 and the sum of its n terms is 255. If its common ratio is 2, then its first term is

1. 1

2. 3

3. 8

4. none of these

Q.

The seventh term of a G.P. is 8 times the fourth term and 5th term is 48. Find the G.P.

Q.

Find the 4th term from the end of the G.P. $\frac{1}{2},\frac{1}{6},\frac{1}{18},\frac{1}{54},.......,\frac{1}{4374}$.

Q.

Find the common difference of an A.P whose first term is unity and whose second, tenth and thirty fourth terms are in G.P

1. $\frac{1}{5}$

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

3. $\frac{1}{6}$

4. $\frac{1}{9}$

Q.

If sum of an infinite geometric series is $\frac{4}{3}$ and $1^{\mathrm{st}}$ term is $\frac{3}{4}$, then its common ratio is

1. $\frac{7}{16}$

2. $\frac{9}{16}$

3. $\frac{1}{9}$

4. $\frac{7}{9}$

Q.

If $S_n=\frac{1}{6\times 11}+\frac{1}{11\times 16}+\frac{1}{16\times 21}.............$up to $n$ terms, then $6S_n$ equals

1. $\frac{\left(5n-4\right)}{\left(5n+6\right)}$

2. $\frac{n}{\left(5n+6\right)}$

3. $\frac{\left(2n-1\right)}{\left(5n+6\right)}$

4. $\frac{1}{\left(5n+6\right)}$

Q.

The fifth term of a G.P. is 81 whereas its second term is 24. Find the series and sum of its first eight terms.

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.

A minimum value of integral from $0$ to $xt{e}^{-t^2}dt$ is

1. $1$

2. $2$

3. $3$

4. $0$

Q.

The 4th and 7th terms of a G.P. are $\frac{1}{27}$ and $\frac{1}{792}$ respectively. Find the sum of n terms of the G.P.

Q.

The fourth term of a G.P. is 27 and the 7th term is 792, find the G.P.

Q.

The sum of the series $5.05+1.212+0.29088+...........\infty$ is

1. $6.93378$

2. $6.87342$

3. $6.74384$

4. $6.64474$

Q. The converse of the statement "If $x+2=6,$ then $x=4$" is

1. If $x\ne 4,$ then $x+2=6$
2. If $x\ne 4,$ then $x+2\ne 6$
3. If $x+2\ne 6,$ then $x\ne 4$
4. If $x=4,$ then $x+2=6$

Q.

A number consists of three digits which are in GP the sum of the right-hand digits exceeds twice the middle digits by $1$ and the sum of the left-hand and middle digits is two-third of the sum of the middle and right-hand digits. Find the number.

Q.

If in an infinite G.P first term is equal to the twice of the sum of the remaining terms, then common ratio is

1. $1$

2. $2$

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

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

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. $\frac{1}{64}$
4. $\frac{1}{128}$

Q.

The sum of the perimeter of a circle and square is k, where k is some constant, Prove that the sum of their areas is least when the side of square is double the radius of the circle.