# How do you find the first five terms of the sequence a_1=3, a_(n+1)=2a_n-1?

Nov 6, 2016

3,5, 9,17,33

#### Explanation:

${a}_{n + 1} = 2 {a}_{n} - 1$
So if ${a}_{n} = 3$ then ${a}_{n + 1}$=. 2 x 3 - 1. = 5

${a}_{n + 1}$ is the next term in the sequence after ${a}_{n}$
And ${a}_{n} = 5$ then ${a}_{n + 1}$=. 2 x 5 - 1 = 9
${a}_{n} = 9$ then ${a}_{n + 1}$ =2 x 9 - 1 = 17
And the next term 2 x 17 - 1 = 33

The sequence increases by powers of 2!