Question

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

Answer 1

We know aₙ = a₁ + (n-1)d
Thus a₂₁ = a₁ + 20d
and a₇ = a₁ + 6d

Thus a₂₁ - a₇ = (a₁ + 20d) - (a₁ + 6d)
= 14d

According to question a₂₁ - a₇ = 84
∴ 14d = 84
or, d = 6


Thus the common difference is 6.

Answer 2

Hi there !

a₂₁ - a₇ = 84

we know that ,

$a_{n} - a_{k} = (n - k)d$

here , d = common difference

so ,

a₂₁ - a₇ = 84

(21 - 7)d = 84
14d = 84

d = 84/14
   = 6

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Common difference = d = 6