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

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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:

$26 = a_{7}$

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

$\Rightarrow 26 = 8 + 6 d$

$\Rightarrow d = 3$

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

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

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

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

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

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

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