Question

Does 301 appear in the sequence 5, 11, 17, 23,........?​

Answer 1

$5 \: \: \: \: 11 \: \: \: \: \: 17 \: \: \: 23........ \\ \\ a = 5 \: \: \: \: \: \: d = 6 \\ \\ tn = 301 \\ \\ tn = a + (n - 1)d \\ \\ 301 = 5 + (n - 1)6 \\ \\ 301 = 5 + 6n - 6 \\ \\ 301 = 6n - 1 \\ \\ 301 + 1 = 6n \\ \\ 302 = 6n \\ \\ n = \frac{302}{6} \\ \\ n = \frac{151}{3} \pink{not \: \: \: equal \: \: \: to \: \: \: natural \: \: no.} \\ \\ \blue{301 \: \: \: is \: \: \: not \: \: \: belongs \: \: \: to \: \: \: given \: seris}$

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Answer 2

                                Hello

As you can see, all the number differ by 6.

This means the pattern is like this, 5,11,17,23,29,35,41.........

You can notice that all the numbers are 1 less than a number divisible by 3 So, by that method 299 will be one of the number in the sequence.(300 is divisible by 6 and so 300-1=299)

Thus, after 299 the number will be 305,311,317...........

So 301 does not appear in the sequence.