Question

The sum of all even natural numbers less than hundred is____??​

Answer 1

★ Given :

A.P : 2, 4, 6, 8, 10 .............. 98

First tern (a) = 2

Common Difference (d) = 2

Last term (An or L) = 98

_________________________

★ To Find :

Sum of all even terms less than 100.

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★ Solution :

We know that,

$\Large{\boxed{\boxed{\purple{\sf{A_{n} = a + (n - 1)d}}}}}$

98 = 2 + (n - 1)2

98 = 2 + 2n - 2

98 = 2n

98/2 = n

49 = n

$\large{\boxed{\blue{\sf{Number \: of \: terms \: (n) = 49}}}}$

Now,

$\Large{\boxed{\boxed{\orange{\sf{S_{n} = \frac{n}{2}(a + L)}}}}}$

(Putting Values)

$\begin{gathered}\sf{s_{n} = \frac{49}{2}(2 + 98) } \\ \\ \sf{s_{n} = \frac{49}{ \cancel{2}}( \cancel{100}) } \\ \\ \sf{s_{n} = 49 \times 50 } \\ \\ \sf{s_{n} = 2450}\end{gathered}$

$\large{\boxed{\red{\sf{S_{n} = 2450}}}}$