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

This is the sum of the arithmetic sequence:
 10 - 2 + 6 + 14 + ... + 110
where:  a 1 = - 10, d = 8
a n = 110
a n = a 1 + ( n - 1 ) * d
110 = - 10 + ( n - 1 ) * 8
110 = - 10 + 8 n - 8
110 + 10 + 8 = 8 n
128 = 8 n
n = 128 : 8
n = 16
∑ n = n/2 * ( a 1 + a n ) 
∑ 16 = 16/2 * ( -10 + 110 ) = 8 * 100 = 800

The sum is 800.

Opposite angles in a cyclic quadrilateral add up to 180°