Nth Term of a GP

Q. Which term of the progression $20,19\frac{1}{4},18\frac{1}{2},17\frac{3}{4}$..is the first negative term?

Q.

Given two finite sets A and B such that n(A) = 2, n(B) = 3. Then total number of relations from A to B is ___.

Q.

The $4^{th}$ and the $9^{th}$ term of a G. P. are 8 and 256 respectively. Find the G. P.

1. 1, 9, 15, 20, 26

2. 1, 3, 5, 8, 16

3. 1, 2, 4, 8, 16

4. 2, 4, 8, 16, 36

Q.

Which term of the sequences $\sqrt{3},3,3\sqrt{3},....\mathrm{is}729?$

Q.

If x, 2x + 2, 3x + 3, are in G.P., then the fourth term is _____.

1. 13.5

2. -13.5

3. -27

4. 27

Q.

Find the ${11}^{\mathrm{th}}$ term of the GP :$3,6,12,24,\dots .$

Q.

Write the first three terms in each of the sequences defined by the following -
(i) $a_n$ = 3n + 2
(ii)$a_n$ = $n^2$ + 1

Q.

Second term of a geometric progression is 6 and its fifth term is 9 times of its third term. Find the geometric progression. Consider that each term of the G.P. is positive.

Q.

the sum of four consecutive terms of A.P is 2 .The sum of 3rd and 4th terms is 11. Find the terms

Q. What is the 6th term in the GP series: 1, 2, 4...?

1. 16
2. 32
3. 128
4. 64

Q. If we have given that in a g.p.the first term is exceed 2nd term by 35 and 3 rd term exceeds 4 th term by 516 ten find four successive term of that g.p

Q.

Find the 9th term of the series :

1, 4, 16, 64, ......................

Q.

$7^{\text{th}}$ term of the sequence
$\sqrt{2},\sqrt{10},5\sqrt{2},.........$ is ___.

1. $25\sqrt{2}$

2. $125\sqrt{2}$

3. 125

4. $125\sqrt{10}$

Q. $\sqrt{3},\frac{1}{\left(\sqrt{3}\right)},\frac{1}{3\left(\sqrt{3}\right)}.....$
The ${19}^{\text{th}}$ term of the above sequence is .

1. $\frac{\sqrt{3}}{3^{18}}$
2. $\frac{3^{15}}{2}$
3. $\frac{\sqrt{3^7}}{3^{26}}$

Q.

If the first term of a G.P. is 5 and the common ratio is -5, then 3125 is the ____ term.

1. $6^{th}$

2. $5^{th}$

3. $8^{th}$

4. $7^{th}$

Q.

Four Geometric means are inserted between 2 and 486. Find the common ratio of the resulting G.P.

1. 3

2. 4

3. 2

4. 5

Q.

If 17th term of an A.P. exceeds the 13th term by 15 , find common difference.

Q.

The first two terms of a G.P. are 125 and 25 respectively. Find the $5^{th}$ and the $6^{th}$ terms of the G.P.

Q.

The product of $3^{rd}$ and $8^{th}$ terms of a G.P. is 243. If its $4^{th}$ term is 3, find its $7^{th}$ term.

Q.

The fifth term of a G.P. is 81 and its second term is 24. Find the geometric progression.

Q. The seats in an arena are arranged so that each row is longer than the row in front of it by the same number of seats. The 13th row has 71 seats and the 19th row has 95 seats. Determine the total number of seats in the front three rows combined.

Q.

The sum of n terms of the series $2^2+4^2+6^2+..........is$

Q.

Given the terms $a_{10}=\frac{3}{512}$ and $a_{15}=\frac{3}{16384}$ of a geometric sequence, find the exact value of the term $a_{30}$ of the sequence.

1. $a_{30}=3{\left(\frac{1}{2}\right)}^{59}$

2. $a_{30}=3{\left(\frac{1}{2}\right)}^{19}$

3. $a_{30}=3{\left(\frac{1}{2}\right)}^{39}$

4. $a_{30}=3{\left(\frac{1}{2}\right)}^{29}$

Q.

Find the third term from the end of the G.P. $\frac{2}{27},\frac{2}{9},\frac{2}{3},...................,162.$

Q.

If fifth term of a G.P. is 4, then product of first nine terms is

1. 4⁹

2. 18⁴

3. 9⁴

4. 4¹⁸

Q.

Which term of the G.P. :

$-10,\frac{5}{\sqrt{3}},-\frac{5}{6},..........is-\frac{5}{72}?$

Q. A club consists of few members who's ages are in AP, the common difference being 6 months . the youngest member of the club is just 10 years old and the sum of the ages of all the members is 400 years .find the number of members in the club

Q.

If $S$ is the sum of infinite GP & $a$is the first term, then the common ratio $r$ is given by:

1. $\frac{a-S}{S}$

2. $\frac{S-a}{S}$

3. $\frac{a}{1-S}$

4. $\frac{S-a}{a}$

Q. What is the 6th term in the GP series: 1, 2, 4...?

1. 16
2. 128
3. 32
4. 64

Q.

Which term of the following A.P. would be 0?
36, 33, 30, 27….

1. 12

2. 10

3. 9

4. 13