Question

Simplify: 5 + (− 5) + 5 + (− 5) + ...
(i) When the number of terms is 20 (ii) When the number of terms is 25

Answer 1

(i) When the number of terms is 20
5 + (− 5) + 5 + (− 5) + ... = (5 + 5 + 5 + ... + 10 terms) + (− 5) + 5 + (− 5) + ... + 10 terms
= 10 $\text{×}$ 5 + 10 $\text{×}$ (− 5)
= 50 − 50
= 0

(ii) When the number of terms is 25
5 + (− 5) + 5 + (− 5) + ... = (5 + 5 + 5 + ... + 12 terms) + (− 5) + 5 + (− 5) + ... + 13 terms
= 12 $\text{×}$ 5 + 13 $\text{×}$ (− 5)
= 60 − 65
= − (65 − 60)
= − 5