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Question:

What is the common difference of an A.P., in which a21 - a7 = 644?

Solution:

We know that, an = a + (n-1)d
Now, by using the above definition,
a21 - a7 = 644
a + (21-1)d - [a + (7-1)d] = 644
a + 20d - a - 6d = 644
14d = 644
d = 46
So, the common difference of the A.P. is 46.