Problem Solving

36^2 + 37^2 + 38^2 + 39^2 + 40^2 + 41^2 + 42^2 + 43^2 + 44^2 =

A) 14400
B) 14440
C) 14460
D) 14500
E) 14520

Need some help in the approach for this one. I cannot see any obvious sequence/series pattern.

Actually, just realised it is simplified if 40 is taken as a baseline:

36 = (40 - 4) ^ 2
37 = (40 - 3) ^ 2
....
44 = (40 + 4) ^ 2

36^2 = 40^2 - 320 + 16
37^2 = 40^2 - 240 + 9
....
44^2 = 40^2 + 320 + 14

Therefore there are 9*40^2 = 1600 * 9
Sum of 16 + 9 + 4 + 1 = 30

30 * 2 (due to both sides of 40) = 60

= 14400 + 60 = 14460

C

Absolutely great...
This is the most concise solution.
But if u needed a time consuming solution , it would be this.
It would surely take ur 2 mins off.
Use the formula (n(n+1)(2n+1))/6

First compute for first 44 natural numbers..
Second compute for first 35 natural numbers.(In exam time if we didnt remain calm we would go with 36 instead of 35, because of which , this is a dangerous solution).

Subtract both of them.
You will find answer to be C Again

Thanks, that's very helpful.

Great hint. Thanks!