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## What is the common difference of an A.P. in which a21 – a7 = 84? Mathematics CBSE class 10 2017

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

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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.

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