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

Solution:

Let $A_{1}, A_{2}, A_{3}, A_{4}, A_{5}$ be five numbers between 8 and 26 .

Let d be the common difference.

Then, we have:

  26 = a7

$\Rightarrow 26=8+(7-1) d$

$\Rightarrow 26=8+6 d$

$\Rightarrow d=3$

$A_{1}=8+d=8+3=11$

$A_{2}=8+2 d=8+6=14$

$A_{3}=8+3 d=8+9=17$

$A_{4}=8+4 d=8+12=20$

$A_{5}=8+5 d=8+15=23$

Therefore, the five numbers are 11, 14, 17, 20, 23.