Find the 13th term of the sequence 8, -16, 32, -64,

a. 32768

b. -16384

c. -65536

d. none of these

This is a geometric sequence because dividing any term by the previous term results in a constant called the common ratio.  Any geometric sequence can be expressed as:

a(n)=ar^(n-1), a=initial term, r=common ratio, n=term number.

The common ratio,r, is -16/8=32/-16=-64/32=-2, and the first term, a, is 8

So the rule for this sequence is:

a(n)=8(-2)^(n-1), so the 13th term is:

a(13)=8(-2^12)

a(13)=32768