What is the sum of the geometric sequence 5, - 20, 80, - 320?

Answer 1

What is the sum of the geometric sequence: 5, -20, 80, -320

1. technically, since there are only 4 numbers in the sequence, to get the sum you could just add them! :-)
2. 5 + (-20) + 80 + (-320) = -255

But you should know the summation formula for a geometric series too.

1. S_n = a₁(1-rⁿ) / (1-r) ; r ≠ 1
2. a₁ = 5
3. n = 4 (there are 4 terms)
4. r (ratio, or multiplier) = -4; a₂/a₁ = -20/5 = -4
5. S₄ = 5(1-(-4)⁴) / (1-(-4))
6. 5(1-256)/5 = -1275/5 = -255

I hope you understand the process, and commit the summation formula to memory, as the next problem have quite a few terms (too many to manually add in a timely fashion).. :-)

Answer 2

What is the sum of the geometric sequence 5, - 20, 80, - 320?

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The Sum is simply adding all the values together and getting a result.

Sum = 5 + (-20) + 80 + (-320) = - 255.....Is that the value you got?