Question

Check whether 422 is in the sequence 10, 13, 16, 19, 22, ....

Answer 1

Given sequence is 10, 13, 16, 19, 22, .....

Here, t₁ = 10, t₂ = 13, t₃ = 16

Now, t₂ – t₁ = 13 – 10 = 3

And t₃ – t₂ = 16 – 13 = 3

∵ t₂ – t₁ = t₃ – t₂ 

∴ This sequence is an A.P.

So, First term, a = 10

Common Difference, d = 3

Let 422 be its n^th term.

Then, t_n = a + (n – 1)d

⇒ 422 = 10 + (n – 1)3

⇒ 422 = 10 + 3n – 3

⇒ 422 = 7 + 3n

⇒ 422 – 7 = 3n

⇒ 415 = 3n

⇒ n = 138.333

However, it is not an integer.

As a result, 422 is not in the specified sequence.