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algebra intermediate

Problem

The second and ninth terms of an arithmetic sequence are 2 and 30, respectively. What is the fiftieth term?
Solution
Let be the first term, and let be the common difference. Then the term is . In particular, the second term is , and the ninth term is . Subtracting these equations, we get , so . Substituting this into the equation , we get , so .

Then the fiftieth term is .
Final answer
194