Answer:
[tex]a_n=150+50n[/tex]
[tex]a_n=n^2+17n+182[/tex]
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:
[tex]a_n=a+(n-1)d[/tex]
Where, a is first term and d is common difference n is the number of terms:
[tex]a_n=200+(n-1)50[/tex]
[tex]a_n=150+50n[/tex]
Now, for second sequence:
200,220,242,266,292
[tex]a_n=n^2+17n+182[/tex] is the iterative rule
If we put n=1 in above formula we will get [tex]a_n=200[/tex]
At n=2, [tex]a_n=220[/tex]
And so on... by substituting consecutive values as in sequence given.
