Question

what is the iterative rule for each sequence? (show work) 200,250,300,350,400,450 200,220,242,266,292,322

Answer 1

`a_n=150+50n`

`a_n=n^2+17n+182`

Explanation:

We have been given two sequence:

200,250,300,350,400,450

200,220,242,266,292,320

In first sequence We can see that there is common difference of 50 between consecutive terms:

So, we can use the formula of arithmetic sequance which is:

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

Where, a is first term and d is common difference n is the number of terms:

`a_n=200+(n-1)50`

`a_n=150+50n`

Now, for second sequence:

200,220,242,266,292

`a_n=n^2+17n+182` is the iterative rule

If we put n=1 in above formula we will get
`a_n=200`

At n=2,
`a_n=220`

And so on... by substituting consecutive values as in sequence given.