Question

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

Answer 1

let a is the first term and d is the common difference of an AP
a21 = a + ( 21 -1)d = a + 20d
a7 = a + (7 -1)d = a + 6d

now,
a +20d -a -6d = 84

14d = 84

d = 6 ( answer)

Answer 2

solution:-

here, given a21 - a7 = 84 .................. ( 1 )


let the first term of the AP be a and the common difference be d.

an = a+ ( n-1) d

a21 = a+ ( 21- 1) d = a + 20d
a7 = a + ( 7 - 1) d= a+ 6d

Substituting the values in equation ( 1 )
a + 20d - ( a + 6d ) = 84
14d = 84
therefore, d= 6 (ans) .