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| 1. |
Find the sum of odd numbers between 0 and 50. |
| Answer» {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}\xa0 | |