Question

Series:

Use the Arithmetic Series formula to calculate the sum:

-6+(-3)+0+ • • • + 162

(Hint: how many numbers are being added?)

Answer 1

Explanation:

The common difference is 3.

nth term = -6+(n-1)3

-6+(n-1)3 = 162

(n-1)3 = 168

n-1 = 56

n = 57

162 is the 57th term.

S₅₇ = 57×(a_1+a_{57})/2

= 57×(-6+162)/2

= 57×156/2

= 57×78

= 57×(-6+162)/2

= 4446