What is the sum of the geometric sequence -4, 24, -144, ... if there are 6 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

a = -4

r = 24/-4 = -6

n = 6

Substituting it in the formula

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

= -4(-6⁶ - 1)/(-6 - 1)

By further calculation

= -4(46656 - 1)/ -7

= -4(46655)/ -7

So we get,

= 186620/7

= 26660

Therefore, the sum of the geometric sequence is 26660.

What is the sum of the geometric sequence -4, 24, -144, ... if there are 6 terms?

Summary:

The sum of the geometric sequence -4, 24, -144, ... if there are 6 terms is 26660.