Question

The first several terms of a sequence {an} are: 12,0,12,0,12,.... Assume that the pattern continues as indicated, find an explicit formula for an.

Answer 1

`a_n=6+(-1)^(n+1)6`

Explanation:

The given sequence is

`12,0,12,0,12,0,...`

Assume that the pattern continues as indicated, the we need to find an explicit formula for the above sequence.

From the given sequence it is clear that all odd terms are 12 and all odd terms are 0.

Half of 12 is 6.

We know that,

`6+6=12`

`6-6=0`

So, the required formula is

`a_n=6+(-1)^(n+1)6`

Therefore,
`a_n=6+(-1)^(n+1)6` .