Question

What are first terms of this sequence: f(1)=-2, f(n)=f(n-1)+4?

Answer 1

`n=1->a_1=-2 larr" given value"`

`n=2->a_2=-2+4 = 2`
`n=3->a_3=-2+4+4 = 6`
`n=4->a_4=-2+4+4+4=10`

Explanation:

Let the place count be `n`
Let the `n^("th")` term be `a_n`

Given `f(n=1)=-2`

We are also told that any one term is the previous term + 4.
This is derived from `f(n)=f(n-1)+4` where `f(n-1)` is the previous term.

Consequently we have an Arithmetic sequence with common difference of +4

From this the sequence is:

`n=1->a_1=-2 larr" given value"`

`n=2->a_2=-2+4 = 2`
`n=3->a_3=-2+4+4 = 6`
`n=4->a_4=-2+4+4+4=10`

And so on. Also from this we also have an alternative equation for any `a_n` in that we have:

`a_n =-2+4(n-1)`