Find the sum of the following (starts with 3, increment by 7, ends with 7N+3)

Question

3+10+17+...+689+696+703

Answer 1

the term of 7N+3 tells me that you want the sum of n terms

sum(n) = (n/2)(2a + (n-1)d )
sum(n) = (n/2)(6 + (n-1)(7))
= (n/2)(6 + 7n - 7)
= n(7n - 1)/2

Answer 2

notice that ... (703 + 3) = (696 + 10) = (689 + 17) ...

so ... sum = (703 + 3) * (101 / 2)

Answer 3

How do you know n is 101?

Answer 4

703 - 3 = 700 ... 700 / 7 = 100

100 terms beyond the 1st term ... a total of 101