Question

Check whether 301 is a term of numbers 5,11,17,23....

Answer 1

a = 5, d = 11-5
d = 6
nth term = 301
a +(n-1)d = 301
5+(n-1)6 =301
5+ 6n-6 = 301
-1+6n = 301
6n = 301+1
6n = 302
n = 302/6 (Divide by 2 )
n = 151/3
so,151/3 is not a term of the given list of number.

Answer 2

Hi!

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Finding Common difference (d) from the list of numbers

5 , 11, 17 , 23 .......

$a_2 - a_1$

= 11 - 5

= 6

$a_3 - a_2$

= 17 -11

= 6

So , We have

First term ( a)  = 5

Common Difference (d)  = 6

nth term = 301

Putting the value in the Formula

$a_n = a + (n-1) d$

$301 = 5 + (n - 1) * 6$

= $301 = 6n - 1$

$n = \frac{302}{6}$

= $\frac{151}{3}$

Here , n is not a positive integer . So , 301 is not a term of the given list of numbers

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Thanks !!