Problem:
Find the eighth term of the sequence , whose terms are formed by multiplying the corresponding terms of two arithmetic sequences.
Solution:
The th term of an arithmetic sequence has the form , so the product of corresponding terms of two arithmetic sequences is a quadratic expression, . Letting , and produces the equations , , and , whose common solution is , , and . Thus the eighth term is . Note that can be used to generate pairs of arithmetic sequences with the desired products, such as and .
The problems on this page are the property of the MAA's American Mathematics Competitions