The average of 7 consecutive numbers is a. If the next two numbers are included, the average will be-

Question: The average of 7 consecutive numbers is a. If the next two numbers are included, the average will be-

Answer:
let first number is n
so, the numbers are n, n+1, n+2,......, n+6
(n + n + 1 + .... + n + 6)/7 = a
⇒ 7n + (1 + 2 + 3 +....+ 6) = 7a
⇒ 7n + (6 × 7)/2 = 7a
⇒ 7n + 21 = 7a
⇒ 7n = 7a - 21
⇒ n = (7a - 21)/7
∴ n = 7(a - 3)/7 = a - 3

If the next two numbers are included, the average will be
= (n + n + 1 + .... + n + 8)/9
= {9n +(1 + 2 + 3 +.....+8)}/9
= (9n + 36)/9
= n + 4
= a - 3 + 4
= a + 1

So, the average will increase by 1