Question

In the sequence generated by the formula an=(-1)^n+1(5)^n, which of the following terms has the greatest value? Assume an > 0.

a. an
b. an+5
c.an+10
d.an+15

Answer 1

C

Explanation:

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Answer 2

c a(n+10)

Explanation:

[(-1)^(n+1)] × (5^n)

an > 0

a(n+5) = (-1)⁵ × 5^(n+5) < 0

a(n+10) = (-1)¹⁰ × 5^(n+10) > 0

a(n+15) = (-1)¹⁵ × 5^(n+15) < 0

Since a^n is positive, n is even

Odd powers of -1 are negative