Question

Write a recursive rule for the sequence an=-4+4n

Answer 1

`a_(1)=0` and

`a_(n)=a_(n-1)+4`

Explanation:

The sequence is given by
`a_(n) =-4+4n`.

Now, putting n = 1,
`a_(1)=-4+4 (1)=0`.

Now, putting n = 2,
`a_(2)=-4+4(2)=4`

Therefore,
`a_(2)=a_(1)+4` .........(1)

Again, putting n = 3,
`a_(3)=-4+4(3) =8`

Therefore,
`a_(3)=a_(2)+4` .......... (2)

Hence, from equations (1) and (2), we can write

`a_(1)=0` and

`a_(n)=a_(n-1)+4`

So, this above relation gives the recursive rule for the given sequence. (Answer)