Question
Check whether 301 is in the sequence
$5,11,17,23, \ldots \text { ? }$
$5,11,17,23, \ldots \text { ? }$
✓
Answer
In the sequence $5,11,17,23, \ldots$
$
\begin{array}{l}
t_1=5, t_2=11, t_3=17, t_4=23, \ldots \\
t_2-t_1=11-5=6 \\
t_3-t_2=17-11=6
\end{array}
$
$\therefore$ This sequence is an A.P.
First term $a=5$ and $d=6$
If 301 is $n^{\text {th }}$ term, then.
$
\begin{array}{l}
t=a+(n-1) d=301 \\
\therefore 301=5+(n-1) \times 6 \\
=5+6 n-6 \\
\therefore 6 n=301+1=302 \\
\end{array}
$
$\therefore n=\frac{302}{6}$. But it is not an integer.
$\therefore 301$ is not in the given sequence.
$
\begin{array}{l}
t_1=5, t_2=11, t_3=17, t_4=23, \ldots \\
t_2-t_1=11-5=6 \\
t_3-t_2=17-11=6
\end{array}
$
$\therefore$ This sequence is an A.P.
First term $a=5$ and $d=6$
If 301 is $n^{\text {th }}$ term, then.
$
\begin{array}{l}
t=a+(n-1) d=301 \\
\therefore 301=5+(n-1) \times 6 \\
=5+6 n-6 \\
\therefore 6 n=301+1=302 \\
\end{array}
$
$\therefore n=\frac{302}{6}$. But it is not an integer.
$\therefore 301$ is not in the given sequence.
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