Math Question from official sat

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1

<p>Hey guys could someone please explain this to me:
5, a, b, 5
In the sequence above, the first term is 5 and the second term is a. Eavh term after the second is the product of the two immediately preceding terms. If a<0 what is the 10th term in the sequence?
A.-5^21
B. -5^10
C. g
D. 5^10
E. 5^21</p>

<p>The answer is E. But how do we get that? Thanks in advance!</p>

2

<p>Well if the sequence is: 5, a, b, 5</p>

<p>then ab=5 and b=5a. Substitute and 5a^2=5, so a=1. Plug that back in so b=5. That would make the sequence…</p>

<p>5, 1, 5, 5, 5^2, 5^3, 5^5, 5^8, 5^13, 5^21.</p>

3

<p>a must be less than 0, but Gmer has the right idea: a = -1, b = -5, and the rest works out to 5^21.</p>

4

<p>Oh whoops, I read that as greater than.</p>