SOLUTION: What is the sigma notation of these series 6-12+24-48+96-192

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Question 1205367: What is the sigma notation of these series 6-12+24-48+96-192
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: sum%286%28-2%29%5E%28k-1%29%2Ck=1%2C6%29

Explanation

The sequence 6, -12, 24, -48, 96, -192 is geometric with
a = 6 = first term
r = -2 = common ratio
We start with 6 and double each term, along with change the sign from positive to negative or vice versa.

In general the nth term of a geometric sequence is a%5Bn%5D+=+a%2A%28r%29%5E%28n-1%29
In this case the nth term is a%5Bn%5D+=+6%28-2%29%5E%28n-1%29
When forming the answer shown above, I used k as the index. But you could use any variable really.
We stop at index k = 6 because a%5B6%5D+=+6%28-2%29%5E%286-1%29+=+-192 or just note how -192 is the 6th term.