Question

Consider the sequence: 3, 8, 13, 18, 23, ...The recursive formula for this sequence is:an = an-1 + 5In a COMPLETE sentence, explain what an and an-1 represent in the formula. Then find a8 . What do you need to know in order to find a8 ?

Answer 1

`a_8=38`

Explanation:

Recursive sequence

In a recursive sequence formula, each term
`a_n` is computed as a function of one or more previous terms. In the formula

`a_n=a_(n-1)+5`

n is the number of the term we want to calculate. If n=8, then the formula becomes

`a_8=a_(7)+5`

We can see
`a_(n-1)` is the previous term. It means we need
`a_7` to be able to compute
`a_8`. But we also need
`a_6` to compute
`a_7` and so on until some known data is reached. The question provides five terms,
`a_5=23.`

`a_6=a_5+5=28`

`a_7=a_6+5=33`

`a_8=a_7+5=38`

`a_8=38`