Question

A supermarket finds that the number of boxes of a new cereal sold increases each week. In the first week, only 20 boxes of the cereal were sold. In the next week, 53 boxes of the cereal were sold and in the third week 86 boxes of the cereal were sold. The number of boxes of cereal sold each week represents an arithmetic sequence.

What is the explicit rule for the arithmetic sequence that defines the number of boxes of cereal sold in week n?




an=33n−13

an=33n+13

​an=33n−53

an=33n+53

Answer 1

20+33(n-1)=an

20+33n-33=an

an=33n-13

Answer 2

Hence, the explicit formula is given as:

an=33n−13

Explanation:

In the first week, only 20 boxes of the cereal were sold. In the next week, 53 boxes of the cereal were sold and in the third week 86 boxes of the cereal were sold.

The number of boxes of cereal sold each week represents an arithmetic sequence.

As the number of boxes represents an arithmetic sequence.

Hence we get a common difference as 'd'.

This means in the second week the number of boxes are given as:

20+d=53

d=53-20

d=33.

Hence, in the third week it is given as:

`a_3=a+2d\\\\a_3=20+2* 33\\\\a_3=86`

Hence, the explicit formula is given as:

an=33n−13

( since, in all the other options at n=1 we did not get a_1=20)