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Question
Find the sum of all even numbers from 1 to 250.
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Solution
The even numbers from 1 to 250 are 2, 4, 6, 8, ............, 250
And the last even number is = 250
∴ an = 250, a = 2 and d = 2
∴ an = a + (n – 1)d
∴ 250 = 2 + (n – 1)2
∴ 250 = 2 + 2n – 2
∴ 2n = 250
∴ n = `250/2` = 125
From 1 to 250, there are 125 even numbers.
Since, we know `S_n = n/2 [a + a_n]`
∴ The sum of 125 even numbers
`S_125 = 125/2 [2 + 250]`
= `125/2 xx 252`
= 125 × 126
= 15,750
As a result, the total of all even numbers from 1 to 250 is 15,750.
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