write the sum using summation notation, assuming the suggested pattern continues. -1+2+5+8+...+44

Answer 1

This is arithmetic sequence: a₁ = - 1 and d = 2 - (- 1) = 3. a_n = a₁ + (n - 1)d = - 1 + (n - 1)·3 = 3n - 4;

3n - 4 = 44; 3n = 48; n = 16

-1 + 2 + 5 + 8 + ...+ 44 = ∑₁¹⁶(3n - 4)