Question

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

Answer 1

Let $A_1,A_2,A_3,A_{4}and{A}_5$ be five numbers betw een 8 and 26, Such that 8, $A_1,A_2,A_3,A_4,A_5,$26 are A.P.

Here a = 8, let the common difference of A.P. be 'd'.

Then $a_7$ = 26

$\therefore a+(7-1)d=26\Rightarrow 8+6d=28$

$\Rightarrow 6d=26-8\Rightarrow d=\frac{26-8}{6}=3$

Now,

$A_1=a+d=8+3=11$

$A_2=a+2d=8+2\times 3=8+6=14$

$A_3=a+3d=8+3\times 3=8+9=17$

$A_4=a+4d=8+4\times 3=8+12=20$

$A_5=a+5d=8+5\times 3=8+15=14$

Thus, the five numbers between 8 and 26 are 11, 14, 17, 20 and 23.