In a geometric sequence, the first term is 3 and the common ratio is -2. What is the sum of the first 6 terms?
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Correct answer
A. -63
Principle or equation
The sum of the first n terms of a geometric sequence is S_n = a(1 - r^n)/(1 - r) for r ≠ 1.
Why this answer is correct
Here a=3, r=-2, n=6. S_6 = 3(1 - (-2)^6)/(1 - (-2)) = 3(1 - 64)/3 = 3(-63)/3 = -63.
Example
For a=2, r=3, n=4, S_4 = 2(1-81)/(1-3) = 80.
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