Find the sum of the first 25 terms of a geometric sequence where the first term is 177,147 and the common ratio is -1/3
Mathematics · Middle School · Tue Nov 03 2020
Answered on
Given:
1st term: 117, 147
Common Ratio: - ⅓
Determine the sum of the first 25 terms of the geometric sequence.
Formula for geometric sequence:
An = A1 ( r )^(n-1)
Formula for the sum of geometric sequence:
Sn = (a1 (r^n -1))/ r - 1
Solution:
Substitute the given values to the formula for the sum of geometric sequence.
S25 = (117, 147(1- (-⅓)^25 ))/ 1 - (-⅓)
S25 = (117, 147(1- (-⅓)^25 ))/ 1 + ⅓
S25 = 87860.25
Final answer:
S25 = 87860.25