Question

Write the sum using summation notation assuming the suggested pattern continues. -8-3+2+7+...+67

Answer 1

You can use the generic representation of a term of an arithmetic sequence:

`a_n=a_1+d(n-1)`
Filling in the values a₁=-8, d=5, you have

`a_n=-8+5(n-1)\\a_n=-13+5n`

Then the value of n for the last term can be found as
67 = -13 + 5n
80 = 5n
16 = n
and the sum can be written as


`S_(16)=\sum\limits_(n=1)^(16){(-13+5n)}`