Question

If a1=2 and an=2an-1 find the first 5 sequences

Answer 1

The first 5 terms of the sequence are 2, 4, 8, 16 and 32.

Explanation:

Given:

`a_(1)` = 2

`a_(n)` = 2
`a_(n-1)` -----------------(i)

To get the first 5 terms of the sequence, substitute in turn, n = 1, 2, 3, 4, 5 into equation (i).

The first term (when n = 1) has been given as:

`a_(1)` = 2

The second term (when n = 2) is given as:

`a_(2)` = 2
`a_(2-1)`

`a_(2)` = 2
`a_(1)` (but
`a_(1)` = 2 )

=>
`a_(2)` = 2(2)

=>
`a_(2)` = 4

The third term (when n = 3) is given as:

`a_(3)` = 2
`a_(3-1)`

`a_(3)` = 2
`a_(2)` (but
`a_(2)` = 4 )

=>
`a_(3)` = 2(4)

=>
`a_(3)` = 8

The fourth term (when n = 4) is given as:

`a_(4)` = 2
`a_(4-1)`

`a_(4)` = 2
`a_(3)` (but
`a_(3)` = 8 )

=>
`a_(4)` = 2(8)

=>
`a_(4)` = 16

The fifth term (when n = 5) is given as:

`a_(5)` = 2
`a_(5-1)`

`a_(5)` = 2
`a_(4)` (but
`a_(4)` = 16 )

=>
`a_(5)` = 2(16)

=>
`a_(5)` = 32

Therefore, the first 5 terms of the sequence are 2, 4, 8, 16 and 32.