What is the commo

Let the common difference be 'd' and the first term be 'a'.

And we know that, nth term of an AP is given by

a_n = a + (n - 1) d

where n is the nth term
a is the first term
d is the common difference

Given:  a₂₁ - a₇ = 84

a₂₁ = a + (21 - 1) d                                  .........eq(1)

a₇ = a + (7 - 1) d                             .................eq(2)


Subtracting eq (2) from eq(1):

a₂₁ - a₇ = a + 20d - (a + 6d) = 84

   ⇒ 14d = 84

 

   ⇒ d = 6

Hence, the common difference of AP is 6.