What is the sum of the geometric sequence -4, 24, -144, ... if there are 8 terms?

Solution:

The formula to find the sum of geometric sequence is a(rⁿ - 1)/(r - 1)

Where a is the first number, r is the common ratio, and n is the number of terms

It is given that geometric sequence -4, 24, -144,...8 terms

⇒ a = -4

⇒ r = 24/-4 = -6

⇒ n = 8

Substituting it in the formula, we get

Sum of the geometric sequence = a(rⁿ - 1)/(r - 1)

= -4(-6⁸ - 1)/(-6 - 1)

By further calculation

= -4(1679616 - 1)/ -7

= -4 (1679615)/-7

So we get,

= 6718460/7

= 959780

Therefore, the sum of the geometric sequence is 959780.

Summary:

The sum of the geometric sequence -4, 24, -144, ... if there are 8 terms is 959780.