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Arithmetic Progressions — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSArithmetic Progressions2 Marks
Question
The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1. Find the first term and the common difference.
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Answer

Given, $\text{a}=3\text{a}_1\ .....(1)$ $\text{a}_7=2\text{a}_3+1\ .....(2)$ Expandind (1) and (2) $\text{a}+3\text{d}=2\text{a}$ $\therefore2\text{a}=3\text{d}$ or $\text{a}=\frac{3\text{d}}{2}\ .....(3)$ $\text{a}+6\text{d}=2\text{a}+4\text{d}+1$ $\text{a}+1=2\text{d}\ .....{(4)}$ From (3) and (4) $\text{a}=3$ and $\text{d}=2$

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