# math

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An arithmetic series has third term 11. The ninth term is 5 times the second term. Find the common difference.

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Let the first term be called a and the common difference be called b.
a + 2b = 11
a + 8b = 5*(a + b) = 5a + 5b
The last equation can be rewritten
4a - 3b = 0
4a + 8b = 44
11b = 44
b = 4
a = 11 - 2b = 3
The series is 3,7,11,15,19,23,27,31,35...
Note that 35 (the ninth term) is 5 times 7

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