SOLUTION: The eighth term of an arithmetic sequence is 55 and the tenth term is 77. Find the third term.

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Question 463762: The eighth term of an arithmetic sequence is 55 and the tenth term is 77. Find the third term.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
a%5B8%5D+=+a%5B3%5D+%2B+%288-3%29d+=+a%5B3%5D+%2B+5d+=+55
and
a%5B10%5D+=+a%5B3%5D+%2B+%2810-3%29d+=+a%5B3%5D+%2B+7d+=+77
Subtracting the top equation from the bottom equation, we get 2d = 22, or d = 11.
Hence a%5B3%5D+%2B+5%2A11+=+55, or a%5B3%5D+=+0.