A sequence is defined by the recursive function f (n + 1) = - 10f (n). if f (1) = 1, what is f (3)

3

-30

100

-1000

This is a geometric sequence because each term is - 10 time the previous term.

All geometric sequences have the rule:

a (n) = ar^ (n-1), a=1st term, r=common ratio, n=term number, in this case:

a (n) = 1 (-10) ^ (n-1) so a (3) is:

a (3) = 1 (-10) ^2

a (3) = 1 (100)

a (3) = 100