Question

Find the sum of the even numbers from 26 to 126

Answer 1

3,876

Explanation:

Sequence of even numbers from 26 to 126 is given as:

26, 28, 30, 32, 35..............,126

Here, a = 26, d = 2,
`a_n = 126`

`\because a_n = a + (n-1)d\\</p><p>\therefore 126 = 26 + (n-1) * 2\\</p><p>\therefore 126 - 26 = 2(n-1) \\</p><p>\therefore 100= 2(n-1)\\</p><p>n - 1 = (100)/(2) \\</p><p>n - 1 = 50\\</p><p>n = 50 +1\\</p><p>\red{\bold{n = 51}}`

`</p><p>\because S_n = (n)/(2)(a + a_n) \\\\</p><p>\therefore S_(51)= (51)/(2)(26 + 126) \\\\</p><p>\therefore S_(51)= (51)/(2)* 152 \\\\</p><p>\therefore S_(51)= 51* 76 \\\\</p><p>\huge \purple {\boxed {\therefore S_(51)=3,876}} </p><p>`

Answer 2

3876

Explanation:

Here first even number is 26

and last even number is 126

we add both of these and divide the sum by 2

26 + 126 = 152

152/2 = 76

now there are total 51 even number from 26 to 126.

so sum of even numbers from 26 to 126 is

sum = 76 × 51 = 3876