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Find the sum of odd numbers …

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Find the sum of odd numbers between 0 and 50.

Posted by Ramana Murthi 7 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Prabjeet Singh 7 years, 5 months ago

{tex}\text {Series of odd is }1, 3, 5, ..., 49.{/tex}

{tex}\therefore \text { first number } a = 1 \text { last number } l = 49{/tex}

{tex}a_n=a+(n-1)d{/tex}

{tex}\Rightarrow 49=1+(n-1)(2){/tex}

{tex}\Rightarrow n=25{/tex}

{tex}\text {Total odd numbers from 0 to 50 are}{/tex}

{tex}\text {Now, sum of odd numbers from 1 to 50 } S_n \text { is }{/tex}

{tex}S_n = \cfrac {n}{2}(a+l){/tex}

{tex}\Rightarrow S_n = \cfrac {25}{2} (1+49){/tex}

{tex}\Rightarrow S_n = 25 \times 25=625{/tex}

{tex}\text {Thus, required sum is 625.}{/tex}

0Thank You

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