Question

For each of the squences below, find a formula that generates the sequence.

(a) 10,20,10,20,10,20,10...

Answer 1

`a_(n)=15 + (-1)^n * 5`

Explanation:

First, we notice that the when n is odd,
`a_(n)` = 10. And when n is even,
`a_(n)` = 20.

The average of 10 and 20 is
`(10+20)/2 = 15`. So, the distance between 15 and 10 is the same that between 15 and 20.

That distance is 5.

From 15, we need to subtract 5 to get 10 when n is odd and we need to add 5 to get 20 when n is even.

The easiest way to express that oscilation is using
`(-1)^n`, because it is (-1) when n is odd and 1 when is even. And when multiplied by 5, it will add or subtract 5 as we wanted.