Question

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

Answer 1

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

Given a21.

Then a21 = a + (21 - 1) * d

                = a + 20d     --------------------- (1)


Then a7 = a + (7 - 1) * d

              = a + 6d           -------------------- (2)


Given that (1) and (2) = 84

= (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!

Answer 2

a21-a7 = 84
a21 = a+20d
a7 = a+6d
a+20d-a-6d= 84
14d= 84
d= 84/14
d=6

hope it helps! :)