Find the sum of the geometric series 81 - 108 + 144 - … + 256

Answer:Identify the PatternThe first term (a) is 81.The common ratio ® is -108/81 = -4/3 (each term is multiplied by -4/3 to get the next term)Find the Number of Terms (n)We need to figure out how many terms are in the series. Let’s find the term number for 256: 81 * (-4/3)^n = 256 (-4/3)^n = 256/81 = (4/3)^4 n = 4There are 4 terms in the series.Apply the Geometric Series FormulaThe sum (S) of a finite geometric series is:S = a(1 - r^n) / (1 - r) S = 81 (1 - (-4/3)^4) / (1 - (-4/3)) S = 81 (1 - 256/81) / (7/3) S = 81 (-175/81) / (7/3) S = -175 * (3/7) S = -75Therefore, the sum of the geometric series 81 - 108 + 144 - … + 256 is -75.

Answered by alixzamarirapacon | 2024-09-10