If the differences are same the formula is this:
a+(n-1)d,
a is the first term of the sequence and
d is the common difference between the numbers. n is our term number and we plug the term number instead of
n to find the value of the term.
If the differences are changing then we use this formula:
nth term =
a + (n - 1)d + ½(n - 1)(n - 2)cThis time there is a letter
c which stands for the second difference (or the difference between the differences and d is just the difference between the first two numbers.
Ok so we will use the 2nd formula to your question since the difference between the numbers are changing:
the difference is: 9,11,13,15
the difference between the differences:2,2,2,2
a=17
d=9(difference between the first two numbers,17 and 26)
c=2(the difference between the differences)
plug in these values into the formula:
a + (n - 1)d + ½(n - 1)(n - 2)c
17+(n-1)9+1/2(n-1)(n-2)2
simplify it and u will get:
n^2+6n+10In order to see if ur formula is right u can do it like this:
nth term=1---> 1^2 +6(1)+10=17
nth term=2---> 2^2 +6(2)+10=26
nth term=3---> 3^2 +6(3)+10=37
I hope you will get it