Question

What is the sum of the first five terms of a geometric series with a1 = 6 and r = 1/3? Express your answer as an improper fraction in lowest terms without using spaces.

Answer 1

242/27

Explanation:

Using the formula for the sum, you can fill in the given values and do the arithmetic.

Sn = a1·(r^n -1)/(r -1)

S5 = 6·((1/3)^5 -1)/(1/3 -1) = 6(-242/243)/(-2/3) = 6·(121/81)

S5 = 242/27

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Or, you can write the terms and add them up. The sum is ...

6 + 2 + 2/3 + 2/9 + 2/27 = (162 +54 +18 +6 +2)/27 = 242/27