Tough level 5 math question

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1

<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>
2

<p>nevermind I got it</p>

3

<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>

4

<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>