Question

Which of the following recursive formulas represents the same arithmetic sequence as the explicit formula an = 2 + (n – 1)5?

Answer 1

2+6-1*5       =35 n=6        I'm not 100% positive

Answer 2

The recursive formulas for the following sequence is
`a_n=a_(n-1)+5`.

Explanation:

The given explicit formula is

`a_n=2+(n-1)5`

Find the (n-1)th term of the sequence.

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

`a_(n-1)=2+(n-2)5` .... (1)

The given explicit formula can be written as

`a_n=2+(n-1(-2+2))5`

`a_n=2+(n-2(-1+2))5`

`a_n=2+(n-2+1)5`

Use distributive property.

`a_n=2+(n-2)5+5`

Using equation (1), we get

`a_n=a_(n-1)+5`

Therefore the recursive formulas for the following sequence is
`a_n=a_(n-1)+5`.