Question

Insert five numbers between $8$ and $26$ such that the resulting sequence is an A.P.

Answer 1

Step $1:$ Finding common difference.

Let $A_1,A_2,A_3,A_4$ and $A_5$ be five numbers between $8$ and $26$ such that $8,A_1,A_2,A_3,A_4,A_5,26$ are in A.P.
Here, $a=8,b=26,n=7$ and $d=\text{common difference}$

As we know, $b=a+(n-1)d$
$\Rightarrow d=\frac{b-a}{n-1}$
$\Rightarrow d=\frac{26-8}{7-1}=\frac{18}{6}=3$

Step $2:$ Finding numbers between $8$ and $26$.
Thus,
$A_1=a+d=8+3=11$
$A_2=a+2d=8+2\times 3=8+6=14$
$A_3=a+3d=8+3\times 3=8+9=17$
$A_4=a+4d=8+4\times 3=8+12=20$
$A_5=a+5d=8+5\times 3=8+15=23$

Final answer: Hence, the required five numbers between $8$ and $26$ are $11,14,17,20$ and $23$.