In a geometric sequence, the second term is 6 and the fifth term is 48. What is the sum of the first 6 terms?
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Correct answer
C. 189
Principle or equation
For a geometric sequence, a_n = a_1 * r^(n-1). Use given terms to find a_1 and r, then sum S_n = a_1 * (r^n - 1)/(r - 1) for r ≠ 1.
Why this answer is correct
Let a_1 be the first term and r the common ratio. a_2 = a_1 r = 6, a_5 = a_1 r^4 = 48. Dividing the second by the first: r^3 = 8, so r = 2. Then a_1 = 6/2 = 3. Sum of first 6 terms: S_6 = 3 * (2^6 - 1)/(2 - 1) = 3 * 63 = 189.
Example
If a_1 = 2 and r = 3, the first 4 terms are 2, 6, 18, 54; sum = 80.
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