College Algebra Math

Question

Consider the following sequence 5,−15,45,−135,405,...Write an explicit formula for the sequence.

(use the form an=b(r)^n−1)

Answer 1

Note there is a common ratio of -3:

-15/5 = -3

45/-15 = -3

-135/45 = -3

405/-135 = -3

Therefore, you have a geometric series. If the first term is a₁, then

a₂ = -3a₁

a₃ = (-3)²a₁

a₄ = (-3)³a₁

Can you see the pattern?

a_n = (-3)^n-1 a₁