<p>In the sequence above, the first term i s3 and each following term is 3 times the term before it. Of the following, which is an expression for the 100th term of the sequence?
A. 3(99)
B. 3(100)
C. 3(100)+3
D.3^100
E. 100^3</p>
<ol>
<li><p>Jason uses two different mixtures of windshield washer fluid for his car. In summer the mixture is one part washer fluid to one part water. How many ounces of washer fluid should Jason add to 24 ounces of the summer mixture in order to produce the winter mixture?
A. 3
B. 12
C. 30
D. 36
E. 48</p></li>
<li><p>If (x+y)(x^2-y^2) = 0, which of the following must be true?
A. x = y
B. x = -y
C. x^2 = y^2
D. x^2 = -y^2
E. x^3 = y^3</p></li>
</ol>
<p>Do you notice a pattern?
Each term is 3^n where n is the nth term of the sequence. (Ex. 1st term is 3^1 = 3, 2nd term is 3^2 = 9 and so on…)
Therefore, the 100th term is expressed as 3^100.</p>
<ol>
<li>Since the first number is 3 and all numbers are multiplied by 3 then the pattern is really just adding 1 to the exponent each time. The pattern really is: 3^1, 3^2, 3^3, 3^4…</li>
</ol>
<p>So the 100th term would be 3^100 so the answer is D</p>
<ol>
<li><p>Is there more info for number 2? You need to know the ratio of water to washer fluid in winter to determine how much needs to be added.</p></li>
<li><p>Since the answer is 0, either x+y=0 or x^2-y^2=0. Only one of these has to be true. For the first equation, this means that x has to be the opposite of y. So if x is 2, y has to be -2. For the second equation, x^2 has to equal y^2. So if x was 2, y could be 2 or -2 and it would end up equaling 0.</p></li>
</ol>
<p>The question asks what MUST be true. So I went through and found which ones could be false.</p>
<p>A: A can be false because x can be 2 and y can be -2 and the first equation would be 0
B: B can be false because x and y could both be 2 and the second equation would be 0
C: This one is always true because if x and y are the same, then the squares will be the same. If x and y are opposites (2 and -2) then the squares would still be the same.
D: This one can never be true because you cannot have a negative after squaring a number
E: If x=2 and y=-2 then this one is false.</p>
<ol>
<li>Jason uses two different mixtures of windshield washer fluid for his car. In summer the mixture is one part washer fluid to three parts water; in winter the mixture is two parts washer fluid to one part water. How many ounces of washer fluid should Jason add to 24 ounces of the summer mixture in order to produce the winter mixture?
A. 3
B. 12
C. 30
D. 36
E. 48</li>
</ol>
<p>So the summer mixture is 24 ounces. The ratio makes that 6 ounces of washer fluid to 18 ounces of water (1:3 ratio).</p>
<p>The winger mixture needs twice as much washer fluid as water. Currently there are 18 ounces of water so you need 36 to make it the winter mixture. To get 36 ounces of washer fluid you need to add 30 ounces.</p>