The first term of a geometric sequence is 2 and the common ratio is -3. What is the sum of the first 6 terms?
Show the answer and explanation
Correct answer
A. -364
Principle or equation
For a geometric sequence with first term a and common ratio r, the sum of the first n terms is S_n = a(1 - r^n)/(1 - r) for r ≠ 1.
Why this answer is correct
Here a = 2, r = -3, n = 6. Compute r^6 = (-3)^6 = 729. Then S_6 = 2(1 - 729)/(1 - (-3)) = 2(-728)/4 = -1456/4 = -364.
Example
For a = 1, r = 2, n = 5: S_5 = 1(1 - 32)/(1 - 2) = 31.
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