Question

The graph shows the first five terms in a geometric sequence.

What is the iterative rule for the sequence?

Geometric sequences graph

Responses

an=0.5⋅(8)n−1

a subscript n end subscript equals 0.5 times open parentheses 8 close parentheses to the power of n minus 1 end exponent

an=8⋅(0.5)n

a subscript n end subscript equals 8 times open parentheses 0.5 close parentheses to the power of n

an=8⋅(0.5)n−1

a subscript n end subscript equals 8 times open parentheses 0.5 close parentheses to the power of n minus 1 end exponent

an=8−(0.5)n

a subscript n end subscript equals 8 minus open parentheses 0.5 close parentheses to the power of n

Answer 1

The sequence halves each term starting at 8. Iterative rule:
a1 = 8, a_n = 0.5·a_{n−1} for n ≥ 2.

(Closed form: a_n = 8·(0.5)^{\,n−1}.)