Q:

Write the explicit formula for the geometric sequence. Then find the fifth term in the sequence. a1 = -4, a2 = 8, a3 = -16A. an = -4 x (2)^n; -64B. an = -4 x (-2)^n-1; -64C. an = -4 x (-2)^n; 128D. an = -2 x (-4)^n-1; -512

Accepted Solution

A:
Sequence: -4, 8, -16

rate of increase: -16/8 = -2
Β 
If you make A1 the first term in the sequence you must use (n-1) in the explicit formula. If you go backwards in the sequence to find A0 = 2 then you would use n.

The don't have A0 = 2 listed as an option so we use A1 = -4 and (n-1) terms.

An = -4(-2)^(n-1)

Solving for the 5th term A5, use n = 5

A5 = -4(-2)^(5-1)
A5 = -4(16)
A5 = -64

So the answer is B.