Practice Quiz

SAT Math

Category - Number and Operations

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What is the fourth element of the geometric series where S_5 = 363 and q = 3?
  1. 51
  2. 63
  3. 75
  4. 81
  5. 99
Explanation
Answer: D - The fourth element of the geometric series is 81.
S_n = a_1 (q^n-1)/(q-1)⟺363 = a_1 (3^5-1)/(3-1)⟺363 = a_1 (243-1)/2⟺363 = a_1 242/2⟺
⟺363 = a_1×121⟺a_1 = 363/121⟺a_1 = 3
a_n = a_1×q^(n-1)⟺a_4 = 3×3^(4-1) = 3×3^3 = 3^4 = 81
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