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SAT Prep

Category - Math

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What is the sum of first four elements of the geometric series where a_1 = 20 and q = 1/2?

37.5
40
42.5
45
47.5

Explanation

Answer: A - The sum of first four elements of the geometric series is 37.5. There are 4 elements and n = 4.
S_n = a_1 (1-q^n)/(1-q) = 20×(1-(1/2)⁴)/(1-1/2) = 20×(1-1/16)/(1/2) = 20×(15/16)/(1/2) = 20×15/8 = 75/2 = 37.5

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