$Find the sum of integers from 1 to 50 which are divisible by 2.$
[3 marks]

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Solution

$Integers divisible by 2 (Up to 50) = 2, 4, 6, \dots, 48, 50$
[1 mark]

So, required sum $= 2 + 4 + 6 + . . . . . + 48 + 50 = 2 (1 + 2 + 3 + . . . .24 + 25)$
Here, $n = 25$
Using formula, the sum of first n-natural number
$= \frac{n \times (n + 1)}{2}$
[1 mark]

$∴ 2 (1 + 2 + 3 + . . . .24 + 25) = 2 [\frac{25 \times (25 + 1)}{2}] = 2 \times 25 \times 13 = 650$
[1 mark]

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Find the sum of integers from 1 to 50 which are divisible by 2. [3 marks]

Integers divisible by 2(Up to 50)=2,4,6,⋯,48,50 [1 mark] So, required sum =2+4+6+.....+48+50=2(1+2+3+....24+25) Here, n=25 Using formula, the sum of first n-natural number =n×(n+1)2 [1 mark] ∴ 2(1+2+3+....24+25)=2[25×(25+1)2]=2×25×13=650 [1 mark]

$Find the sum of integers from 1 to 50 which are divisible by 2.$
[3 marks]