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

Answer:

$a_n=150+50n$

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

Step-by-step 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.