Math

Alpha writes the infinite arithmetic sequence 10, 8, 6, 4, 2, 0...

Beta writes the infinite geometric sequence 9, 6, 4, 8/3, 16/9,...

Gamma makes a sequence whose n^th term is the product of the n^th term of Alpha's sequence and the n^th term of Beta's sequence: 10*9,8*6,6*4,4*8/3,2*16/9,...

What is the sum of Gamma's entire sequence?

I know this is a really long question but I need help.

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1. Starting with n=0,
An = 10-2n
Bn = 9*(2/3)^n
Gn = 18(5-n)*(2/3)^n

By the ratio test, the series converges.
Sum = 162

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2. I really don't know the answer?

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