The average of 101 consecutive odd numbers is 303. Find the largest number.
Answer & explanation
Correct answer: option 3
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