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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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