Question

Insert 7 A.M.s between 2 and 17.

Answer 1

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:

$d=\frac{17-2}{7+1}=\frac{15}{8}$

$A_1=2+d=2+\frac{15}{8}=\frac{31}{8}$

$A_2=2+2d=2+\frac{15}{4}=\frac{23}{4}$

$A_3=2+3d=2+\frac{45}{8}=\frac{61}{8}$

$A_4=2+4d=2+\frac{15}{2}=\frac{19}{2}$

$A_5=2+5d=2+\frac{75}{8}=\frac{91}{8}$

$A_6=2+6d=2+\frac{45}{4}=\frac{53}{4}$

$A_7=2+7d=2+\frac{105}{8}=\frac{121}{8}$

Hence, the required A.M.s are $\frac{31}{8},\frac{23}{4},\frac{61}{8},\frac{19}{2},\frac{91}{8},\frac{53}{4},\frac{121}{8}$