# What is the common difference of an AP if the first term is 2 and the fifth term is 14 ?

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For an arithmetic progression, the nth term is given by: a + (n - 1)*d , where a is the first term and d is the common difference.

Here the first term is given as 2 and we have the fifth term as 14

So we have 14 = 2 + (5 - 1)*d

=> 14 = 2 + 4d

=> 14 - 2 = 4d

=> 12 = 4d

=> d = 3

**The required common difference is 3.**

We'll determine the common difference of the arithmetical progression, writting the general term of the sequence.

an = a1 + (n-1)*d

a1 is the first term and d is the common difference

We'll substitute an by a5 and we'll get:

a5 = a1 + 4d

We'll substract a1:

a5 - a1 = 4d

d = (a5 - a1)/4

We'll substitute the given values for a5 and a1:

d = (14-2)/4

d = 12/4

d = 3

**The common difference of the given arithmetical progression is d = 3.**