Question

If the first term of an A.P. is a and nth term is b, then its common difference is

विकल्प

• \[\frac{b - a}{n + 1}\]

   

• \[\frac{b - a}{n - 1}\]

   

• \[\frac{b - a}{n}\]

   

• \[\frac{b + a}{n - 1}\]

   

Answer 1

Here, we are given the first term of the A.P. as a and the n^th term (a_n) as b. So, let us take the common difference of the A.P. as d.

Now, as we know,

a_n = a + ( n-1) d

On substituting the values given in the question, we get.

            b = a + ( n - 1) d 

( n - 1) d = b - a

          d = \[\frac{b - a}{n - 1}\]

Therefore,        d = \[\frac{b - a}{n - 1}\]