Question

Write a recursive formula for the sequence 7, 13, 19, 25, 31 then find the next term in the sequence?

Answer 1

recursive formula:
`a_n=a_(n-1)+6`

next term in the sequence:
`a_1=7;37`

hope this helps! :)

Answer 2

The recursive formula is

`f(1)=7`

`f(n)=f(n-1)+6`

and the next term is in the sequence is 37.

Explanation:

We first have to find a pattern in the numbers we are given. We notice that each number is 6 greater than the previous; for example 13 is 7+6, 19 is 13+6 and so on. Mathematically we write this as

`f(n)= f(n-1)+7`

Where
`f(n)` is the value of nth term of the sequence.

The sequence starts at 7, therefore the first term in the sequence is:

`f(1)=7`

Now the next term (it will be 6th term) of the sequence will be 6 greater than the previous term, and since the previous term is 31, we have:

`f(6)=f(5)+6=31+6=37.`.

Thus the next term in the sequence is 37, and the recursive formula is

`f(1)=7`

`f(n)=f(n-1)+6.`