What is the sum of the geometric sequence 3, 12, 48, … if there are 8 terms?

Solution:

When the ratio between any two consecutive terms in a sequence is the same, it is called a geometric progression.

The general term of any geometric progression = a r^(n-1)

a = 1st term = 3

r = Common ratio = 4

n = Number of terms = 8

Sum of geometric progression with common ratio r can be calculated using the formula

⇒ \((S)_{n}\) = a (1 - rⁿ ) / 1 - r 

⇒ \((S)_{8}\) = 3 (1 - 4⁸ ) / 1 - 4

⇒ \((S)_{8}\)= 3 × (-65536) / ( -3)

⇒ \((S)_{8}\) = 3 × 21845.34

⇒ \((S)_{8}\) = 65536

Thus, the sum of 8 terms of the G.P is 65536.

What is the sum of the geometric sequence 3, 12, 48, … if there are 8 terms?

Summary:

The sum of the geometric progression 3, 12, 48, … if there are 8 terms is 65536.