Question

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

Answer 1

3,5, 9,17,33

Explanation:

`a_(n+1)=2a_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!