Question

Applying the formula for the sum of the first n integers? a-Evaluate 2+4+6+......+500​

Answer 1

Answer:

$S_{250} = 62750$

Explanation:

Given

$Sequence: 2 + 4 + 6 + ..... + 500$

Required

Evaluate the sequence

The sequence shows an arithmetic progression and will be solved using the sum of n terms of an Arithmetic Sequence as follows:

$S_n = \frac{n}{2}(a + L)$

But first, we need to determine the value of n as follows:

$L = a + (n - 1)d$

Where

$L = Last\ Term = 500$

$a = First\ Term = 2$

$d = Common\ Difference = 4 - 2 = 2$

So:

$L = a + (n - 1)d$

$500 = 2 + (n - 1) * 2$

Open bracket

$500 = 2 + 2n - 2$

Collect Like Terms

$2n = 500 + 2 - 2$

$2n = 500$

Divide through by 2

$n = 250$

So:

$S_n = \frac{n}{2}(a + L)$ becomes

$S_{250} = \frac{250}{2}(2 + 500)$

$S_{250} = 125(2 + 500)$

$S_{250} = 125(502)$

$S_{250} = 125 * 502$

$S_{250} = 62750$

Hence, the sum of the sequence is 62750