<p>5, a, b, 5...</p>
<p>In the sequence above, the first term is 5 and the second term is a. Each term after the second is the product of the two immediately preceding terms. If a < 0, what is the 10th term of the sequence?</p>
<p>A) -5^21
B) -5^10
C) 5
D) 5^10
E) 5^21</p>
<p>This is a simple question. If a < 0, then a = -1.
b = -5 because 5 x a = -1 = -5.
-5 x -1 = 5, which is the fourth term. Keep following the rule until you get to the 10th number.
Something logically sequential like this on the Math section usually can’t be done without a calculator unless you want to proceed slowly and run out time at the end.</p>
<p>5, a, b, 5</p>
<p>a < 0</p>
<p>“Each term after the second is the product of the two immediately preceding terms”</p>
<p>Therefore:</p>
<p>b = 5a
5 = ab</p>
<p>Solve for a:
5 = ab
b = 5/a
b = 5a
5/a = 5a
5 = 5a^2
1 = a^2
Since a < 0, a = -1</p>
<p>5, a, b, 5…
5, -1, b, 5…
b = -5</p>
<hr>
<p>5, a, b, 5…
5, a, b, 5, 5b, (5^2)b, (5^3)b^2, (5^5)b^3, (5^8)b^5, <a href=“5%5E13”>b</a>b^8**</p>
<p>Since b = -5, the 10th term is (5^13)((-5)^8), or <a href=“E”>b</a> 5^21**</p>