Sum of the geometric series with a1 = 3, r = 2, n = 4.

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Multiple Choice

Sum of the geometric series with a1 = 3, r = 2, n = 4.

Explanation:
The sum of a finite geometric series uses the formula S_n = a1 (r^n − 1) / (r − 1) for r ≠ 1. With a1 = 3, r = 2, and n = 4, compute r^n = 2^4 = 16. Then S_4 = 3 (16 − 1) / (2 − 1) = 3 × 15 / 1 = 45. The four terms are 3, 6, 12, and 24, which add up to 45. So the sum is 45.

The sum of a finite geometric series uses the formula S_n = a1 (r^n − 1) / (r − 1) for r ≠ 1. With a1 = 3, r = 2, and n = 4, compute r^n = 2^4 = 16. Then S_4 = 3 (16 − 1) / (2 − 1) = 3 × 15 / 1 = 45. The four terms are 3, 6, 12, and 24, which add up to 45. So the sum is 45.

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