# Find the first terms of this sequence: f(1)=-2, f(n)=f(n-1)+4

Find the first terms of this sequence: f(1)=-2, f(n)=f(n-1)+4
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Annabella Ferguson
Let the place count be n
Let the ${n}^{\text{th}}$ 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:

$n=1\to {a}_{1}=-2←\phantom{\rule{1ex}{0ex}}\text{given value}$

$n=2\to {a}_{2}=-2+4=2$
$n=3\to {a}_{3}=-2+4+4=6$
$n=4\to {a}_{4}=-2+4+4+4=10$

And so on. Also from this we also have an alternative equation for any ${a}_{n}$ in that we have:

${a}_{n}=-2+4\left(n-1\right)$