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

c a (n+10)

Step-by-step 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