Solve :

Is 301 any term of the sequence of numbers 5, 11, 17, 23… ?

The arithmetic progression is 5, 11, 17, 23, ….
Here, First term a = 5 and common difference = 11 – 5 = 6
Let us assume that n^th term a_n of the progression is 301.
Since, a_n = a + (n -1)d

Where,

a = First term of AP
d = Common difference of AP
and no of terms is ‘n’

∴ 301 = 5 + (n – 1) × (6)
⇒ 301 = 5 + 6n -6
⇒ 302 = 6n
⇒ n = 50.33
Here n is a fraction, But any term n should be an integer.
∴ 301 is not any term of the arithmetic progression.

Hence, 301 is not any term of the progression.