Question

Write the explicit formula that represents the geometric sequence -2, 8, -32, 128

Answer 1

Explanation:

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Answer 2

The Geometric Sequence Formula:

`a_n=a_1r^(n-1)`

We have:

`a_1=-2,\ a_2=8,\ a_3=-32,\ a_4=128,\ ...`

`d=(a_(n+1))/(a_n)\to d=(8)/(-2)=-4`

Substitute:

`a_n=-22\cdot(-4)^(n-1)=-22\cdot(-4)^n\cdot(-4)^(-1)=-22\cdot(-4)^n\cdot\left(-(1)/(4)\right)=5.5(-4)^n`