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Arithmetic Progressions — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSArithmetic Progressions3 Marks
Question
The third term of an A.P. is 7 and the seventh term exceeds three times the third term by 2. find the first term, the first term, the common difference and sum of first 20 terms.
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Answer

Given, $\text{a}_3=7=\text{a}+2\text{d}\ .....{(1)}$ $\text{a}_7=3\text{a}_3+2$ $\therefore\text{a}_7=3(7)+2$ $[\because\text{a}_3=7]$ $=23=\text{a}+6\text{d}\ .....{}(2)$ Solving (1) and (2) $\text{a}=-1,\text{d}=4$ Then, sum of 20 terms of this A.P $\Rightarrow\text{s}_{20}=\frac{20}{2}[2+(20-1)4]$ $\Big[$ Using $\text{s}_\text{n}=\frac{\text{n}}{2}[2\text{a}+(\text{n}-1)\text{d}\Big]$ $=10\times74$ $=740$

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