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Arithmetic Progressions — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSArithmetic Progressions3 Marks
Question
The sum of first 7 terms of an A.P. is 10 and that next 7 terms is 17. find the progression.
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Answer

Given, $\text{a}_7=10$ $\text{s}_{14}-\text{s}_7=17\ .....{(1)}$ $\therefore\text{s}_{14}=17+\text{s}_7=17+10=27\ .....{(2)}$ From (1) and (2) $\text{s}_7=\frac{7}{2}[2\text{a}+(7-1)\text{d}]$ $\Big[$Using $\text{s}_\text{n}=\frac{\text{n}}{2}[2\text{a}+(\text{n}-1)\text{d}]\Big]$ $\Rightarrow10=7\text{a}+21\text{d}\ .....(3)$ and $\text{s}_{14}=\frac{14}{2}[2\text{a}+13\text{d}]$ $\Rightarrow27=28\text{a}+182\text{d}\ .....{4}$ Solving (3) and (4) $\text{a}=1$ and $\text{d}=\frac{1}{7}$ $\therefore$ The required A.P is $1,\ 1+\frac{1}{7},\ 2+\frac{2}{7},\ 1+\frac{3}{7},...,\ +\infty$ or $1,\ \frac{8}{7},\ \frac{9}{7},\ \frac{10}{7},\ \frac{11}{7},\ ...,\ \infty$

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