Arithmetic Progression

1.        Find the average of all 5 digit numbers that leave a remainder of 2 when divided by 7.

Answer:

Smallest 5 digit number leaving a Remainder of 2 is 10005

Where t₁₄₂₉ = 10005

The largest 5 digit number leaving a Remainder of 2 is 99997

Where t₁₄₂₈₅ = 99997

Sum S = n/2 (t_1429­ + t₁₄₂₈₅)

Or Average = S/n = (t_1429­ + t₁₄₂₈₅) / 2 = (10005 + 99997) / 2 = 55001