Question

write out the sum using the summation notation, assuming the suggested pattern continues. -10-2+6+14+...+110

Answer 1

The series is an arithmetic series with first term -10 and common difference (-2-(-10))=8. The general term a_n can be written as
  a_n = -10 + 8(n-1)
or
  a_n = -18+8n

The last term corresponds to
  110 = -18+8n
  128 = 8n
  16 = n

So, the summation can be written as
$S_{16}=\sum\limits_{n=1}^{16}{(-18+8n)}$

Answer 2

 The answer is summation of the quantity negative ten plus eight n from n equals zero to fifteen