Gujarat BoardEnglish MediumSTD 11 ScienceMATHSArithmetic Progressions2 Marks
Question
Find the sun of all odd numbers between 100 and 200.
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Answer
The series so formed is 101, 103, 105, ... , 199 Let number of terms be n then, $\text{a}_\text{n}=\text{a}+(\text{n}-1)2$ $\Rightarrow199=101+(\text{n}-1)2$ $\Rightarrow\text{n}=50$ The sum of n terms $=\text{s}_\text{n}=\frac{\text{n}}{2}[\text{a}+\text{l}]$ $\text{s}_{50}=\frac{50}{2}[101+199]$ $=7500$ The sum of odd numbers between 100 and 200 is 7500.
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