Question

Which of the following is the formula for the geometric sequence? 320, 80, 20, 5,...

A. an = 320(1/4)n-1
B. an = 320(4)n-1
C. an = 4(320)n-1

Answer 1

First find the common ratio:


r = (any term but the first)/(previous term)


r = (20)/(80)


r = 1/4


So the common ratio is 1/4. Basically, we divide each term by 4 to get the next term


The first term is 320. This is a[1]. So a[1] = 320


In general, the geometric sequence has the following form


a[n] = a[1]*r^(n-1)


Plug in the values we found above to get


a[n] = 320*(1/4)^(n-1)


So the answer is choice A