Write an expression for the apparent nth term an of the sequence. (Assume that n begins with 1.)

Question

-10/11 , 11/12, -12/13, 13/14, -14/15, ...

a(n) =

Answer 1

You need a way of oscillating between positive and negative. One way to do that is to use (-1)n. When "n" is an odd number, like 1, 3, 5, 7, etc) then the term is -1 and if "n" is even, then the term is +1.

So a(n) = (-1)ⁿ•(n + 9)/(n + 10)

Answer 2

then nth term is a fraction where the numerator is one less than the denominator

and the signs alternate

a1 = -10/11

an = [(-1)^n](n+9)/(n+10)