Question

18. The table shows the amount of money in a savings account after several weeks.

Week
au AWN
Savings
$125
$140
$155
$170
$185
$200
a. Is the sequence arithmetic or geometric? Explain Find the common difference or common ratio.
b. Write a recursive formula for the sequence.
c. Write an explicit formula for the sequence.

Answer 1

a. Arithmetic

b.
`a_(n) = a_(n-1) + 15`

c.
`a_(n) = 15n + 125`

Explanation:

A sequence is arithmetic when the difference between one term and the next is a constant. On the other hand, a sequence is geometric when the next term is found by multiplying the previous by a constant.

In this case, the next term of the sequence can be found by adding $15. Therefore, the sequence is ARITHMETIC ✔️

The recursive formula will be the following:
`a_(n) = a_(n-1) + 15`

The explicit formula is the following:
`a_(n) = 15n + 125`