Practice Quiz

SAT Math

Category - Number and Operations

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What is the sum of first four elements of the geometric series where a_1 = 20 and q = 1/2?
  1. 37.5
  2. 40
  3. 42.5
  4. 45
  5. 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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