Answer:
3,876
Step-by-step explanation:
Sequence of even numbers from 26 to 126 is given as:
26, 28, 30, 32, 35..............,126
Here, a = 26, d = 2, [tex] a_n = 126[/tex]
[tex] \because a_n = a + (n-1)d\\
\therefore 126 = 26 + (n-1) \times 2\\
\therefore 126 - 26 = 2(n-1) \\
\therefore 100= 2(n-1)\\
n - 1 = \frac{100}{2} \\
n - 1 = 50\\
n = 50 +1\\
\red{\bold{n = 51}}[/tex]
[tex]
\because S_n = \frac{n}{2}(a + a_n) \\\\
\therefore S_{51}= \frac{51}{2}(26 + 126) \\\\
\therefore S_{51}= \frac{51}{2}\times 152 \\\\
\therefore S_{51}= 51\times 76 \\\\
\huge \purple {\boxed {\therefore S_{51}=3,876}}
[/tex]
