Sum of Squares?

Question

What's the formula for finding the sum of a sequence of squared numbers?
such as,
26^2+27^2+28^2+...100^2

DO NOT give me the formula where the first number is one!!!!! that's what I keep finding when surfing the web for it.

Answer 1

If you already have the formula where the first number is one -- then you should be able to gifure out the answer on your own.

Let F(n) equal the sum of all the squares from one through 'n'.

Then doesn't F(100) - F(25) give you the answer that you need?

Answer 2

Let N be the first number in the sequence that you want to start with.

Let X be the ending number of the sequence (X>N).

The sum of the squares between X to N (X^2 to N^2)would be solved in parts.

First find the sum of squares from 1 to X (1^2 to X^2).

Second find the sum of squares from 1 to [N-1] (1^2 to N-1]^2).

Then subtract the sum of squares from 1 to [N-1] from the sum of squares from 1 to X.

Answer 3

Well, you can always subtract the sum of 1^2 + 2^2 + 3^2 + ... + 25^2. Does this help?