Question

Find the next two terms in this sequence. 1 3 7 15 [?] 2'4'8' 16' T'I

Answer 1

We will solve as follows:

*First: We identify the pattern, that is:

`(3)/(4)-(1)/(2)=(1)/(4)`
`(7)/(8)-(3)/(4)=(1)/(8)`
`(15)/(16)-(7)/(8)=(1)/(16)`

From this, we can see tat the pattern follows the rule:

`((1)/(2))^(n+1)`

So, the next terms of the sequence will be:

`(15)/(16)+((1)/(2))^(4+1)=(31)/(32)`

And the next one is:

`(31)/(32)+((1)/(2))^(5+1)=(63)/(64)`

And those are the next two terms of the sequence.