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