Question

what is the common difference of an ap in which a21-a7=84

Answer 1

in this
(a+20d)-(a+6d)=84
a+20d-a-6d=84
14d=84
d=6
so the common difference is 6
hope this help u

Answer 2

We know that sum of n terms of an AP an = a + (n - 1) * d.

Given a21 - a7 = 84.     ----------------- (1)

a21 = a + (21 - 1) * d

       = a + 20d.    ----------- (2)


a7 = a + (7 - 1) * d

     = a + 6d        ----------- (3)


Substitute (2) & (3) in (1), we get

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

a + 20d - a - 6d = 84

14d = 84

d = 84/14

d = 6.

Therefore the common difference = 6.


Hope this helps!