Question

Which value is the 14th term of the sequence

1/81, 1/27, 1/9, 1/3, 1

A. 6561
B. 59049
C. 2187
D. 19683

Answer 1

This is a geometric sequence because it has a common ratio, denoted r, meaning that each term is a multiple of the previous term.


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

In this case a=
`1 \over 81` and r=3 (because each term is 3 time the previous term) so


`a(n)=(1/81)*3^(n-1)`

So the 14th term is:

a(14)=(1/81)
`*3^(14)`=59049