# Math

1. The fourth and seventh terms of a geometric sequence are 6 and 384, respectively. What is the common ratio and the sixth term of the sequence?

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

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1. 384/6 = 64
There are three terms, so r = 4
T6 = T4*r^2 = 6*16 = 96

r^3 = 8!/7! = 8
so, r=2
T1 = T5/r^4 = 7!/16 = 315

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