Question

what is the common difference of an A.P. in which a21 - a7 = 84?

Answer 1

a21 = a + (21-1)d

a21 = a + 20d

Similarly,

a7 = a + 6d

Now,

a21 - a7 = 84

=> (a + 20d) - ( a+ 6d) = 84

=> a + 20d - a - 6d = 84

=> 14d = 84

=> d = 6

Common difference = 6

Answer 2

Here is the solution :

In general nth term of an A.P = a(First term) + (n-1)*d(Common difference),

Let first term = a,
And Common difference = d,

=> 21st term or a21 = a + 20d,
=> 7th terms or a7 = a + 6d,

From the Question,

We can write,
a + 20d - a - 6d = 84,
=> 14d = 84,
=> d = 84/14 = 42/7 = 6,

Therefore : The Common difference of the A.P is 6,

Hope you understand, Have a great day !
Thanking you, Bunti 360 !!