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

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