Common Ratio

Q.

If the sum of first three terms of a G.P. is $\frac{39}{10}$ and their product is 1, then. its common ratio is $\frac{5}{2}or\frac{2}{5}$

1. True

2. False

Q.

If the sum of m terms of an A.P. is the same as the sum of its n terms, show that the sum of its (m + n) terms is zero.

Q.

The sum of three numbers in G.P. is $\frac{39}{10}$ and their product is 1. Find the numbers.

Q.

If $3^{rd}$ term of a G.P is 36 and $5^{th}$ term is 324, find its Common Ratio (r > 0)

1. r=3

2. r=9

3. r=4

4. r=8

Q. The first term of a geometric series is $375$ and the fourth term is $192$. Find the common ratio and the sum of the first $14$ terms. [4 Marks]

Q.

If $14:35::4:\mathrm{x}$, find the value of $\mathrm{x}$.

Q.

(a) Find the first term of G.P. in which S₆ = 1365 and r = 4

(b) Find the common ratio of a G.P. in which S₂ = 6 and a = 2

Q. Let P and Q be respectively the sum of first 20 terms and the sum of first 40 terms of the series 1 + 4 + 3 + 8 + 5 + 12 + ….. The value of Q – P equals

माना P व Q श्रेणी 1 + 4 + 3 + 8 + 5 + 12 + ….. के क्रमशः प्रथम 20 पदों के योगफल तथा प्रथम 40 पदों के योगफल को दर्शाते है। तब Q – P का मान बराबर है

1. 1560
2. 320
3. 920
4. 1240

Q. What is the common ratio in the GP series: 4, 12, 36, 108, ...?

1. 4
2. 3
3. 2
4. 5

Q. If the ratio of sum of n-terms of two different AP’s is (7n – 4) : (5n + 3), then the ratio of their mth term is equal to

Q.

(a) Find the first term of G.P. in which S₆ = 1365 and r = 4

(b) Find the common ratio of a G.P. in which S₂ = 6 and a = 2

Q.

If $a_1$, $a_2$, $a_3$($a_1>0)$ are three successive terms of a G.P. with common ratio r, the value of r for which $a_3>4a_2-3a_1$ is

1. 1 < r <3

2. -3 < r <-1

3. r >3 or r <1

4. none of these

Q. What is the common ratio in the GP series: 4, 12, 36, 108, ...?

1. 4
2. 3
3. 2
4. 5

Q.

Find the next two terms of the series :

2 - 6 + 18 - 54 .......................... .

Q. If the first and last term of a G.P is 2 and 128 respectively with five terms in between then, the common ratio of the G.P is

1. 4
2. 2
3. 6

Q.

If the ratio of the sum of first three terms and the sum of first six terms of a G.P. be 64 : 189, then the common ratio r is _______.

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

2. $\frac{5}{3}$

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

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

Q.

The common ratio of the G.P series 9, 27, 81 is _____.

1. 2

2. 6

3. 9

4. 3

Q. If the first and last term of a G.P is 2 and 128 respectively with five terms in between then, the common ratio of the G.P is

1. 4
2. 2
3. 6

Q. If the ratio of the sum of first three terms and the sum of first six terms of a G.P. be 125 : 152, then the common ratio r is

1. $\frac{5}{3}$
2. $\frac{3}{5}$
3. $\frac{2}{3}$
4. $\frac{3}{2}$

Q. The common ratio of a G.P is 3 and the but term is 486. If the sum of there terms be 728. Find the term

Q. Let $S_k=k=1,2,....100$ denote the sum of the infinite G.P. whose first term is $\frac{k-1}{k!}$ and the common ratio is $\frac{1}{k}$. Then the value of $\frac{{100}^2}{100!}+\sum _{k=1}^{100}|(k^2-3k+1)S_k|$ is

Q.

Solve the equation. Check your solution.

$\frac{2}{9}g=-8$

Q. Solve $-\frac{21}{16}÷\left(\frac{-7}{8}\right)$

Q.

The common ratio of the G.P series 9, 27, 81 is _____.

1. 6

2. 2

3. 3

4. 9

Q.

The common ratio of the G.P series 9, 27, 81 is _____.

1. 2

2. 9

3. 6

4. 3

Q. If (2x - 1) , (4x - 1), (7 + 2x) ... are in G.P, then next term of the sequence is

1. $\frac{125}{3}$
2. $81$
3. $9$
4. $\frac{625}{3}$

Q. Ratio of sum of n terms of two A.P.s is 7n +1: 4n+ 27. Find ratio of their mth terms. Explain in detail with explainaion in sentences

Q.

The ratio of the sum of n terms of two A.P.’s is $(7n+1):(4n+27)$. Find the ratio of their $m^{th}$ terms.