Difference between revisions of "1955 AHSME Problems/Problem 45"
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Revision as of 22:30, 6 July 2018
Problem 45
Given a geometric sequence with the first term and and an arithmetic sequence with the first term . A third sequence is formed by adding corresponding terms of the two given sequences. The sum of the first ten terms of the third sequence is:
Solution
Let our geometric sequence be and let our arithmetic sequence be . We know that This implies that , hence and . Solving this system yields , so or . But since , and . So our two sequences are and , which means the third sequence will be Calculating the sum of the first 10 terms and adding them up yields 978, hence our answer is .