Question

A pizza with one topping costs $11.

Each additional topping costs $2
more. Write a recursive formula
and an explicit formula for the
situation.
explicit formula:
recursive formula:

Answer 1

Given:

A pizza with one topping costs $11. Each additional topping costs $2 more.

To find:

The recursive formula and an explicit formula for the situation.

Solution:

The sequence of costs of pizza is

11, (11+2), (11+2+2), ...

11, 13, 15, ... are in A.P.

Here,

First term: a=11

Common difference: d=2

Explicit formula of an A.P. is

`a_n=a+(n-1)d`

where, a is first term and d is common difference.

`a_n=11+(n-1)2`

`a_n=11+2n-2`

`a_n=9+2n`

Therefore, the explicit formula for the situation is
`a_n=9+2n`.

Recursive formula of an A.P. is

`a_n=a_(n-1)+d`

Where,
`a_1` is first term and d is common difference.

`a_n=a_(n-1)+2`

Where,
`a_1=11`.

Therefore, the required recursive formula is
`a_n=a_(n-1)+2` where
`a_1=11`.