Question

How do I write the terms of the series and find the sum.

4 summation notaion sign (k+6)^2 where k=1 under the summation sign

Answer 1

think of it as a function
f(k) = (k+6)^2 , and consecutive integers only are used for k starting with k = 1.
The results obtained are then added.

so I am assuming you have
(1+6)^2 + (2+6)^2 + (3+6)^2 + (4+6)^2
= 49 + 64 + 81 + 100
= ....

I am assuming the 4 was written above the sigma sign. It indicates the upper value of k

In this case, since there are only 4 terms, you would just add up the terms
If there had been a large number of terms, e.g. k = 46, you would use the sum of an arithmetic series to find the sum