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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?

Respuesta :

Answer:

125250

Step-by-step 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

[tex]1 + 2+3+4+5 + ........ +n =\frac{1}{2} n(n+1)[/tex]

Here in this case n = 500.

So the sum is [tex]1 +2+3+4+5+ ...... + 500 = \frac{1}{2}\times 500 \times (500+1) =250 \times 501 =125250[/tex]. (Answer)

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