Question

Which of the following is the explicit formulas for the geometric sequence?

A. an= 9(1/3)n+1
B. an= 9(3)n-1
C. an= 9(1/3)n-1
D. an= 9(3)n+1

Answer 1

C. an= 9(1/3)n-1

Explanation:

The decreasing curve means the base of the exponential factor is less than 1, eliminating choices B and D. The value of the term is 9 at n=1, so eliminating choice A.

The general form of the n-th term is ...

an = a1·r^(n-1) . . . . first term a1, common ratio r

so we expect to see an exponent of (n-1) when a1 is the value for n=1. If you match the pattern above to the answer choices, you see the only decision required is whether r=3 or r=1/3. The decaying curve of the graph shows you that r < 1, so the choice is r=1/3 and the formula is ...

an = 9(1/3)^(n-1) . . . . . . . parentheses are needed on the exponent