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Question
What is the common difference of an A.P. in which a21 – a7 = 84?
Solution
Let a be the first term and d be the common difference of AP.
We know that
an = a +(n − 1)d
∴ a21 = a +(21 − 1)d = a + 20d
and a7=a + (7 − 1)d = a + 6d
Given:
a21 − a7 = 84
∴ (a + 20d) − (a + 6d) = 84
⇒ a + 20d − a − 6d = 84
⇒14d = 84
⇒ d = 6
Thus, the common difference of the AP is 6
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