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2009 AMC 12B Problem 12

Problem 12 of 25IntermediateAlgebraArithmetic

The fifth and eighth terms of a geometric sequence of real numbers are 7!7! and 8!8! respectively. What is the first term?

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Solution

The eighth term divided by the fifth term is r3=8!7!=8,r^3 = \dfrac{8!}{7!} = 8, so r=2.r = 2. The fifth term is ar4=7!,a r^4 = 7!, so a=7!16=504016=315.a = \dfrac{7!}{16} = \dfrac{5040}{16} = 315. Thus, the correct answer is E.
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Tagged: geometric sequence · factorial

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