Question

Decide whether 301 is term of given sequence 5, 11, 17, 23,.....

Activity :-  Here, d = `square`, therefore this sequence is an A.P.

a = 5, d = `square`

Let nth term of this A.P. be 301.

t_n = a + (n – 1) `square`

301 = 5 + (n – 1) × `square`

301 = 6n – 1

n = `302/6` = `square`

But n is not positive integer.

Therefore, 301 is `square` the term of sequence 5, 11, 17, 23,......

Answer 1

Here, d = 11 – 5 = \[\boxed{6}\], therefore this sequence is an A.P.

a = 5, d = \[\boxed{6}\]

Let nth term of this A.P. be 301.

t_n = a + (n – 1) \[\boxed{\text{d}}\]

∴ 301 = 5 + (n – 1) × \[\boxed{6}\]

∴ 301 = 5 + 6n – 6

∴ 301 = 6n – 1

∴ 6n = 302

∴ n = `302/6` = \[\boxed{\frac{151}{3}}\]

But n is not positive integer.

Therefore, 301 is \[\boxed{\text{not}}\] the term of sequence 5, 11, 17, 23,......