Question:
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.