Which term of the series 5, 8, 11, 14, ...... is 323?

Concept Used:-

The sequence where the common difference between the successive terms is the same is called the Arithmetic Progression (AP).

The nth number term of Arithmetic Progression can be found using the following formula;

⇒ a_n = a + (n – 1) × d

Where, a is the first term, d is the common difference and n is the total terms of AP.

Explanation:-

Given series is 5, 8, 11, 14, ......

It is an Arithmetic Progression, as common difference is the same.

Here, first term, a = 5

Common difference, d = 8 - 5 = 3 

We have to find the term of 323. Suppose this is nth number term. Then, by the above formula,

⇒ an = a + (n – 1) × d

⇒ 323 = 5 + (n – 1) × 3

⇒ 323 - 5 =(n – 1) × 3

⇒ 318 / 3 = (n – 1) 

⇒ 106 + 1 = n

⇒ 107 = n

⇒ n = 107th

So, the 107th term of the given series is 323.

Hence, the correct option is 2.