# How do you find nth term rule for 2,8,32,128,...?

Nov 19, 2016

${a}_{n} = {2}^{2 n - 1}$

#### Explanation:

Consider the given sequence: 2, 8, 32, 128, ...

Notice that each term is an odd power of 2:

${a}_{1} = 2 = {2}^{1}$
${a}_{2} = 8 = {2}^{3}$
${a}_{3} = 32 = {2}^{5}$
${a}_{4} = 128 = {2}^{7}$

In general the sequence of the odd naturals is generated by: $i = \left(2 n - 1\right) \forall n \in \mathbb{N}$

Hence our general term is: ${a}_{n} = {2}^{2 n - 1}$