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Find the sum of the even numbers from 26 to 126

User Ben Karel
by
8.6k points

2 Answers

3 votes

Answer:

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>

User Dno
by
8.3k points
5 votes

Answer:

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

User Carlitos
by
7.7k points

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