find a formula for the sequence

Question

Find a formula for the general term  of the sequence assuming the pattern of the first few terms continues.

Answer 1

First you look at a difference between consectutive terms: 9/4 and 11/16 look for patterns, the denominator is 4^1 followed by 4^2 so the nth term will be 4^n I also look at the numerator and see it is going up by 2. starting at 9. So multiply by 2, then add 7 to get to 9, so it is 2n+7 n=1 is 9 n=2 is 11 ect... Finally, it alternates - + -... (-1)^n will always alternate negative and positive terms Put it together we have

(-1)^n*(2n+7)/(4^n)