Insert five numbers between 8 and 26 such tha | vedclass

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Question

Let $A_{1}, A_{2}, A_{3}, A_{4}$ and $A_{5}$ be five numbers between $8$ and $26$ such that $8, A_{1}, A_{2}, A_{3}, A_{4}, A_{5}, 26$ is an $A.P.$

Vedclass · Accepted Answer

$11,14,17,20,23$

Vedclass · Answer

Let $A_{1}, A_{2}, A_{3}, A_{4}$ and $A_{5}$ be five numbers between $8$ and $26$ such that $8, A_{1}, A_{2}, A_{3}, A_{4}, A_{5}, 26$ is an $A.P.$

Here, $a=8, b=26, n=7$

Therefore, $26=8+(7-1) d$

$\Rightarrow 6 d=26-8=18$

$\Rightarrow d=3$

$A_{1}=a+d=8+3=11$

$A_{2}=a+2 d=8+2 	imes 3=8+6=14$

$A_{3}=a+3 d=8+3 	imes 3=8+9=17$

$A_{4}=a+4 d=8+4 	imes 3=8+12=20$

$A_{5}=a+5 d=8+5 	imes 3=8+15=23$

Thus, the required five numbers between $8$ and $26$ are $11,14,17,20$ and $23 .$

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

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