Question

Which recursively defined function has a first term equal to 15 and a common difference of 3?

Answer 1

The recursively defined function is:

`\left \{ {{f(1)\ =\ 15} \atop {f(n)=f(n-1)+3}} \right.`

Explanation:

A recursively defined function has two parts:

• The smallest argument, usually f (0) or f (1).
• The nth argument, f (n) given f (n - 1), f (n - 2), etc.

`\left \{ {{f(0)\ \text{or}\ f(1)\ =\ a} \atop {f(n)\ =\ f(n-1)\ +\ d}} \right.`

In this case it is provided that:

The first term, f (1) = 15

Common difference, d = 3

Then the recursively defined function in this case is:

`\left \{ {{f(1)\ =\ 15} \atop {f(n)=f(n-1)+3}} \right.`