A sequence is defined by the recursive function f(n + 1) = –10f(n). If f(1) = 1, what is f(3)? 3 –30 100 –1,000

Answer 1

A sequence is a chain of numbers all related. In this case, they are related by the rule "f(n + 1) = –10f(n)". Each number is called a term. Here is what the rule in this sequence means:

Since f(n + 1) is the "next" term and f(n) is the "current" term, to get to the next term, you take the current term and multiply by -10.

When they say f(1) = 1 it means that the first term (term number 1) is 1. When they ask "What is f(3)?", they are asking, "What is the 3rd term?"

Since term #1 is 1, then to find term #2, we multiply 1 by -10. So term #2 is -10. To find term #3, we take term #2 and multiply it by -10, so -10 x -10 = 100. So term #3 is 100