In a geometric sequence, the first term is 2 and the common ratio is 3. What is the sum of the first 5 terms?
Show the answer and explanation
Correct answer
A. 242
Principle or equation
Sum of the first n terms of a geometric sequence: S_n = a(1 - r^n)/(1 - r) for r ≠ 1, where a is the first term and r is the common ratio.
Why this answer is correct
Here a = 2, r = 3, n = 5. S_5 = 2(1 - 3^5)/(1 - 3) = 2(1 - 243)/(-2) = 2(-242)/(-2) = 242.
Example
For a geometric sequence with a=1, r=2, n=4, S_4 = 1(1-2^4)/(1-2) = 15.
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