Question

Find the formulas for the nth term of each sequences

1. 3, 5, 9, 17, ...
2. 2/5, 3/6, 4/7, 5/8, ...

Answer 1

1. 2^n + 1.

2. (n +1)/(n + 4)

Explanation:

1. 3 5 9 17....

3 = 2^1 + 1

5 = 2^2 + 1

9 = 2^3 + 1

17 = 2^4 + 1

Therefore the nth term is

2^n+ 1 .

2. Looking at the fractions we see that:

Numerators are 2, 3, 4 ,5..

and denominators are 5, 6, 7, 8

So the nth term is

(n + 1) / (n + 4)