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

1.	Check whether 301 is a term of the list of numbers 5, 11, 17, 23, . . .
Answer» We have : a₂ – a₁ = 11 – 5 = 6, a₃ – a₂ = 17 – 11 = 6, a₄ – a₃= 23 – 17 = 6 As a_{k + 1} – a_k is the same for k = 1, 2, 3, etc., the given list of numbers is an AP. Now, a = 5 and d = 6. Let 301 be a term, say, the nth term of the this AP. We know that a_n = a + (n – 1) d So, 301 = 5 + (n – 1) × 6 i.e., 301 = 6n – 1 So, n=302/6=151/3 But n should be a positive integer (Why?). So, 301 is not a term of the given list of numbers.

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

Answer»

We have :

a₂ – a₁ = 11 – 5 = 6,

a₃ – a₂ = 17 – 11 = 6, a₄ – a₃= 23 – 17 = 6

As a_{k + 1} – a_k is the same for k = 1, 2, 3, etc., the given list of numbers is an AP.

Now, a = 5 and d = 6.

Let 301 be a term, say, the nth term of the this AP.

We know that

a_n = a + (n – 1) d

So, 301 = 5 + (n – 1) × 6

i.e., 301 = 6n – 1

So, n=302/6=151/3

But n should be a positive integer (Why?). So, 301 is not a term of the given list of numbers.