<p>I was taking a practice math test, and only got this problem incorrect... any help would be appreciated! Thanks!
1) In the sequence: 5,a,b,5.... 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?
a)-5^21
b)-5^10
c)5
d)5^10
e)5^21</p>
<p>nevermind I got it</p>
<p>If anyone is interested in how to get the answer, you can make two equations. First of all, a<em>b=5. Also, 5</em>a=b. So for b plug in 5<em>a and you get a</em>(5*a)=5. The 5s cancel out and u get a^2=1. A then must be -1 because a<0. Then, fill out the pattern. Here is the pattern:
5,-1,-5,5,-25,-125, 3125, -390,625 , -1,220,703,125 , 4.7E14… which is E.</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, (5^13)b^8</p>
<p>Since b = -5, the 10th term is (5^13)((-5)^8), or (E) 5^21</p>