Question

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

Answer 1

Answer:

No, 301 is not a term of this list of numbers.

Step-by-step explanation:

✧ Given:-

   A.P. :- 5,11,17,23,... where a=5, d=6, aₙ=301

✧ To Check:-

  Whether 301 is a term of the above A.P. or not.

✧ Formula Applied:-

• aₙ=a+(n-1)d

✧ Solution:-

    aₙ=a+(n-1)d, where aₙ=301, a=5, d=6.

⇒ 301=5+[(n-1)×(6)]

⇒ 301-5=6n-6

⇒ 296+6=6n

⇒ 302=6n

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

$\implies\boxed{n=50.333...}$

∴ 301 is not a term of this A.P.

Answer 2

Question :–

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

Given :–

1. First term = 5
2. Second term = 11
3. Third term = 17
4. Fourth term = 23

To Find :–

• 301 term of an A.P.

Solution :–

First, we need to find this is an A.P. or not.

So,

Common difference (d) = $\boxed{ a_{2} - a_{1} = a_{3} - a_{2} = a_{4} - a_{3} }$

d = 11 - 5 = 17 - 6 = 23 - 17

d = 6 = 6 = 6

d = 6

d is same so it is an A.P.

✏️ First term always denoted by a.

• a = 5
• d = 6

Let be $\sf {n}^{th}$ term of an A.P.

$\sf {n}^{th}$ = a + (n - 1)d

301 = 5 + (n - 1) 6

301 = 5 + 6n - 6

301 = -1 + 6n

301 + 1 = 6n

302 = 6n

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

$\sf \frac{151}{3} = n$

$\sf n = 50.3333.......$

It is not a positive integers.

Since, 301 is not a term of an A.P.