Question

A store finds that the number of shirts sold increases each week. In the first week, only 15 shirts were sold. In the next week, 22 shirts were sold and in the third week 29 shirts were sold. The number of shirts sold each week represents an arithnetic sequence.

What is the explicit rule for the arithmetic seuquence that defines the number of shirts sold in week n?

Answer 1

Explanation:

Answer 2

`a_n=8+7n`

Explanation:

No. of T-Shirts sold in first week = 15

No. of T-Shirts sold in second week = 22

No. of T-Shirts sold in third week = 29

The number of shirts sold each week represents an arithmetic sequence.

15,22,29,....

So, a = first term = 15

d = common difference = 22-15= 29-22= 7

Formula of nth term :
`a_n=a+(n-1)d`

a is the first term

d is the common difference

n is the number of term

Now substitute the values in the formula :

`a_n=15+(n-1)7`

`a_n=15+7n-7`

`a_n=8+7n`

Where n is the number of weeks

Hence the explicit rule for the arithmetic sequence that defines the number of shirts sold in week n is
`a_n=8+7n`