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Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
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Verified Answer
Let the five numbers be denoted by $T_2, T_3, T_4, T_5, T_6$ and 26 are in A.P.
26 is the $7^{\text {th }}$ term. If $d$ is the common difference Then $\quad T_7=a+(7-1) d$
$\begin{aligned}
&\Rightarrow \quad 26=8+6 d=6 d=26-8=18 \\
&\therefore \quad d=3
\end{aligned}$
$T_2=a+d=8+3=11$
$T_3=a+2 d=8+6=14$
$T_4=a+3 d=8+9=17$
$T_5=a+4 d=8+12=20$
$T_6=a+5 d=8+15=23$
Required five numbers are $11,14,17,20,23$
26 is the $7^{\text {th }}$ term. If $d$ is the common difference Then $\quad T_7=a+(7-1) d$
$\begin{aligned}
&\Rightarrow \quad 26=8+6 d=6 d=26-8=18 \\
&\therefore \quad d=3
\end{aligned}$
$T_2=a+d=8+3=11$
$T_3=a+2 d=8+6=14$
$T_4=a+3 d=8+9=17$
$T_5=a+4 d=8+12=20$
$T_6=a+5 d=8+15=23$
Required five numbers are $11,14,17,20,23$
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