Question

The first term of a G.P. is 3 and the common ratio is 2. Then the sum of first eight terms of the G.P. is

• A. 763
• B. 189
• C. 381
• D. 765
• E. 655

Answer 1

The Correct Option is D

We are given that the first term of the geometric progression (G.P.) is 3 and the common ratio is 2. We are asked to find the sum of the first eight terms of the G.P.

The formula for the sum of the first \(n\) terms of a G.P. is: 

\(S_n = \frac{a(1 - r^n)}{1 - r}\)

where \(a\) is the first term, \(r\) is the common ratio, and \(n\) is the number of terms.

We are given:

• \(a = 3\)
• \(r = 2\)
• \(n = 8\)

Substituting these values into the formula:

\(S_8 = \frac{3(1 - 2^8)}{1 - 2}\)

\(S_8 = \frac{3(1 - 256)}{-1}\)

\(S_8 = \frac{3(-255)}{-1}\)

\(S_8 = 765\)

The sum of the first eight terms of the G.P. is 765.