Question

Kelly cannot remember the formula for the sum of a finite arithmetic sequence, so she is going to try to derive it. Her problem is to find the sum of the numbers 1 to 500. What should she do first?

Answer 1

125250

Explanation:

We have to find the sum of ( 1 + 2 + 3 + 4 + 5 + ........... + 498 + 499 + 500 ) with out using the formula of sum of a finite A.P. series.

We can otherwise remember the formula of sum of first n natural numbers as

`1 + 2+3+4+5 + ........ +n =(1)/(2) n(n+1)`

Here in this case n = 500.

So the sum is
`1 +2+3+4+5+ ...... + 500 = (1)/(2)* 500 * (500+1) =250 * 501 =125250`. (Answer)