Question

A pizza with one topping costs $11.

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 $a_1=11$.