The average of 101 consecutive odd numbers is 303. Find the largest number.

403

Assume, First odd number = (2n+1)

2nd odd number = (2n+1) + (2-1)(2) = 2n + 3

3rd odd number = (2n+1) + (3-1)(2) = 2n + 5

Similarly,

Last (101th) odd number = (2n+1) + (101-1)(2) = 2n + 201

This is an Arithmetic progression, Thus its sum Sn = (N/2) (a+L)

Sn = (101/2) (2n+1 + 2n+201) = (101/2) (4n+202) = 101(2n+101)

Average = Sum/101

303 = 101(2n+101)/101

2n+101 = 303

n = 101

Last Term L, 101th term = 202+201 = 403

The correct answer is Option (3) → 403