Question

Write a recursive rule an explicit rule for the arithmetic sequence 15,22.5,30,37.5

Answer 1

`a_n = a_o +(n-1) d`

`22.5 = 15 +(2-1) d`

`d = 22.5-15 =7.5`

The general expression is:

`a_n = 15+ (n-1)*7.5 , n \geq 1`

Explanation:

For this case we have the following arithmetic sequence given:

15, 22.5, 30,37.5

In order to fidn the recursive rule for this sequence we need to take in count that the general formula for an arithmetic sequence is given by:

`a_n = a_o +(n-1) d`

Where
`a_n` is the nth term
`a_o` the initial value for the sequence and d the common difference. For this case we have that
`a_o =15`

And for the first term we have:

`15= 15 +(1-1)d`

For the second term we have this:

`22.5 = 15 +(2-1) d`

And solving for the value of d we got:

`d = 22.5-15 =7.5`

And for the 3th term we have:

`a_3= 15 +(3-1)*7.5 =30`

And for the 4th term

`a_4 =15 +(4-1)*7.5 =37.5`

So then our expression is correct and would be given by:

`a_n = 15+ (n-1)*7.5 , n \geq 1`