Question

HELP PLEASE!!!

What’s the recursive and explicit formula for an arithmetic sequence we a1=2 and d=-4 ?

Answer 1

The explicid formula of an arithmetic sequence:

`a_n=a_1+(n-1)d`

We have

`a_1=2,\ d=-4`

Substitute:

`a_n=2+(n-1)(-4)` use distributive property

`a_n=2+(-4n)+(-1)(-4)\\\\a_n=2-4n+4\\\\\boxed{a_n=6-4n}`

The recursive formula of an arithmetic sequence:

`\left\{\begin{array}{ccc}a_1=a_1\\a_n=a_(n-1)+d\end{array}\right`

Substitute:

`\left\{\begin{array}{ccc}a_1=2\\a_n=a_(n-1)-4\end{array}\right`