Question

The 1st term in a sequence is 12. The sequence decreases by 17% each term. What was is the recursive function that will represent the situation

Answer 1

`a_n=(83)/(100)*a_(n-1),where\:a_1=12`

Explanation:

If the first term of the sequence is 12, then
`a_1=12`

Since the sequence by 17% each term, there is a common ratio of
`r=1-0.17\\\implies r=(83)/(100)`

Therefore the sequence is a geometric sequence.

The recursive formula is given as:

`a_n=a_(n-1)*r`

We substitute the common ratio to obtain:

`a_n=(83)/(100)*a_(n-1),where\:a_1=12`