Gujarat BoardEnglish MediumSTD 11 ScienceMATHSArithmetic Progressions2 Marks
Question
Show thet the sum of all odd integers between 1 and 1000 wich are divisibleby 3 is 83667.
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Answer
The odd numbers between 1 and 100 divisible by 3 are 3, 9, 15, ..., 999 Let the number of terms be n then, $n^{th}$ term is 999. $\text{a}_\text{n}=\text{a}(\text{n}-1)\text{d}$ $999=3+(\text{n}-1)6$ $\Rightarrow\text{n}-167$ The sum of n terms $\text{s}_\text{n}=\frac{\text{n}}{2}[\text{a}+\text{l}]$ $\Rightarrow\text{s}_{167}=\frac{167}{2}[3+999]$ $=83667$ Hence proved.
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