Write the sum using summation notation, assuming the suggested pattern continues. -9 - 4 + 1 + 6 + ... + 66

Question

Write the sum using summation notation, assuming the suggested pattern continues.

-9 - 4 + 1 + 6 + ... + 66

Answer 1

a1 = -9, AP d=5

an = a1+d(n-1)

an = 66 = -9+5n -5 = 5n -14

5n = 66+14 =80

n = 80/5 = 16th term = 66

sum = n(a1+an)/2 = 16(-9+66)/2 = 8(57) = 456 = sum of all terms -9 to 66

sum symbol = capital Greek letter Sigma, put i=1 at the bottom and 16 on top of Sigma

Sigma(5n-14) from n=1 to 16 = 456