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

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

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Let five numbers be A,B,C,D,E.

Then  AP=8,A,B,C,D,E,26

Here we have,

      a=8,a_7=26,n=7

 \Rightarrow \, \, a+(n-1)d=a_n

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

\Rightarrow \, \, 6d=18

\Rightarrow \, \, d=\frac{18}{6}=3

Thus, we have A=a+d=8+3=11

                      B=a+2d=8+(2)3=8+6=14

                     C=a+3d=8+(3)3=8+9=17

                   D=a+4d=8+(4)3=8+12=20

                  E=a+5d=8+(5)3=8+15=23

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

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