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

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

Step-by-step explanation:

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

The average of 10 and 20 is . 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 , 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.