Answer:
[tex]a_{n}=15 + (-1)^n * 5[/tex]
Step-by-step explanation:
First, we notice that the when n is odd, [tex]a_{n}[/tex] = 10. And when n is even, [tex]a_{n}[/tex] = 20.
The average of 10 and 20 is [tex](10+20)/2 = 15[/tex]. 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 [tex](-1)^n[/tex], 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.
