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Consecutive odd integers whose sum is `25^2-11^2` areA. `n=14`B. `n=16`C. first odd number is 23D. last odd number is 49 |
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Answer» Correct Answer - A::C::D Let n consecutive odd numbers be `2k+1,2k+3,2k+5,"....."2k+2n-1` According to question, sum of these n numbers `=(n)/(2)[2k+1+2k+2n-1]=n(2k+n)` `=n^(2)+2kn=(n+k)^(2)-k^(2)` Given that, `(n+k)^(2)-k^(2)=25^(2)-11^(2)` `implies n+k=25` and `k=11 " "impliesmn=14` and `k=11` So, first term `=2k+1=23` Last term `=2k+2n-1=22+28-1=22+27=49` |
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