CBSE BoardEnglish MediumSTD 11 ScienceMathsArithmetic Progressions2 Marks
Question
Insert $7$ A.M.s between $2$ and $17$.
✓
Answer
Let $A_1, A_2, A_3, A_4, A_5, A_6, A_7$ be the seven A.M.s between $2$ and $17$.
Then, $2, A_1, A_2, A_3, A_4, A_5, A_6, A_7$_ and $17$ are in A.P. whose common difference is as follows:
$\text{d}=\frac{17-2}{7+1}$
$=\frac{15}{8}$
$\text{A}_1=2+\text{d}=2+\frac{15}{8}=\frac{31}{8}$
$\text{A}_2=2+2\text{d}=2+\frac{15}{4}=\frac{23}{4}$
$\text{A}_3=2+3\text{d}=2+\frac{45}{8}=\frac{61}{8}$
$\text{A}_4=2+4\text{d}=2+\frac{15}{2}=\frac{19}{2}$
$\text{A}_5=2+5\text{d}=2+\frac{75}{8}=\frac{91}{8}$
$\text{A}_6=2+6\text{d}=2+\frac{45}{4}=\frac{53}{4}$
$\text{A}_7=2+7\text{d}=2+\frac{105}{8}=\frac{121}{8}$
Hence, the required A.M.S are $\frac{31}{8},\ \frac{23}{4},\ \frac{61}{8},\ \frac{19}{4},\ \frac{91}{8},\ \frac{53}{4},\ \frac{121}{8}.$
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