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