Insert five numbers between $8$ and $26$ such that resulting sequence is an $A.P.$
Insert five numbers between $8$ and $26$ such that resulting sequence is an $A.P.$
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, $26=8+(7-1) d$
$\Rightarrow 6 d=26-8=18$
$\Rightarrow d=3$
$A_{1}=a+d=8+3=11$
$A_{2}=a+2 d=8+2 \times 3=8+6=14$
$A_{3}=a+3 d=8+3 \times 3=8+9=17$
$A_{4}=a+4 d=8+4 \times 3=8+12=20$
$A_{5}=a+5 d=8+5 \times 3=8+15=23$
Thus, the required five numbers between $8$ and $26$ are $11,14,17,20$ and $23 .$
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- [JEE MAIN 2020]