Question

The nth terms of an AP is 6n+2. Find the common difference

Answer 1

Answer :

Common difference , d = 6

Note :

★ A.P. (Arithmetic Progression) : A sequence in which the difference between the consecutive terms are equal is said to be in A.P.

★ If a1 , a2 , a3 , . . . , an are in AP , then

a2 - a1 = a3 - a2 = a4 - a3 = . . .

★ The common difference of an AP is given by ; d = a(n) - a(n-1) .

★ The nth term of an AP is given by ;

a(n) = a + (n - 1)d .

Solution :

• Given : nth term , a(n) = 6n + 2
• To find : Common difference , d = ?

We have ,

a(n) = 6n + 2

Thus ,

=> a(n - 1) = 6(n - 1) + 2

=> a(n - 1) = 6n - 6 + 2

=> a(n - 1) = 6n - 4

Also ,

We know that , the common difference is given by ;

=> d = a(n) - a(n - 1)

=> d = (6n + 2) - (6n - 4)

=> d = 6n + 2 - 6n + 4

=> d = 6

Hence ,

Common difference , d = 6