SOLUTION: the nth term in an arithmetic sequence is represented by tn. If tp=p squared and tq=q squared find the common difference.

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Question 54684: the nth term in an arithmetic sequence is represented by tn. If tp=p squared and tq=q squared find the common difference.
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Let the first term of the A.P. series be 'a' and the common difference be 'd'.
Then, the p-th term is tp+=+a+%2B+%28p-1%29d and q-th term is tq+=+a+%2B+%28q-1%29d.
Given that tp=p%5E2 and tq=q%5E2.
So, p%5E2+=+a+%2B+%28p-1%29d --------(1)
and q%5E2+=+a+%2B+%28q-1%29d --------{2)
Subtracting (2) from (1),
p%5E2-q%5E2=%28p-1%29d+-+%28q-1%29d
or %28p%2Bq%29%28p-q%29=%28p-q%29d
or d+=+p%2Bq [since p is not equal to q]
So the reqd. common difference is (p+q).