Tabbiejack
Write the explicit formula for the geometric sequence.
a1 = -5 a2 = 20 a3 = -80
A. an = -5 • (-4)n
B. an = -5(-4)n-1
C. an = -4(-5)n-1
D. an = -5 • (4)n
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bahrom7893
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look
a1 = -5
n=1
a2=20
n=2, etc..
Jhannybean
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It would be B because in a geometric sequence, you have \[\large ar ^{n-1}\] and in finding our r, we take \(\large\frac{ a _{2} }{ a _{1} }\) and that is -4
bahrom7893
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This way you can eliminate A because term 2 doesn't match up... And I think Jhanny's right
Tabbiejack
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thanks you that was heard
Jhannybean
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So we have a1 = -5, our r = -4 and plug it into our formula \[\large ar ^{n-1}\]
Jhannybean
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thanks bahrom :)
Tabbiejack
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Can you help me with another
Jhannybean
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sure
Tabbiejack
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What is the simplified form of the expression?|dw:1369539526178:dw|
Jhannybean
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Alright, for this one you have a variable with two different powers dividing eachother, and in this case, we can simply do this. \[\large \frac{ 1 }{ q ^{\color{red}{(33/4)-8} }}\]
Jhannybean
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we you know to solve \[\color{fuchsia}{\frac{ 33 }{ 4 }}-\color{green}{8}\]
Tabbiejack
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|dw:1369539985575:dw|
Tabbiejack
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That is the choices
Jhannybean
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hmm...something seems wrong here.
Jhannybean
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\[\frac{ 33 }{ 4 }-8*(\frac{ \color{green}{4} }{ \color{green}{4} })= \frac{ 33 }{ 4 }-\frac{ \color{darkorchid}{32} }{ \color{darkorchid}{4} }\]
Jhannybean
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Ohh I see. hm, well what do you get when you reduce 33/4- 32/4? :D
Tabbiejack
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I am confused
Jhannybean
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hm?
Tabbiejack
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I have no Idea what the answer is
Jhannybean
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solve (33/4)-(32/4) and we'll work from there, you'; get your answer, promise :)
Tabbiejack
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I am the parent of 2 children that is failing
Tabbiejack
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this looks like greek to me..
Jhannybean
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ok, what is.... 3-2?
Tabbiejack
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1
Jhannybean
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good :) so 33-32 works the same way, it is also 1.
Jhannybean
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So we now have \[\frac{ 1 }{ q ^{\color{blue}{1/4}} }\]
Tabbiejack
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o ok
Tabbiejack
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I thank you so much
Tabbiejack
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algebra has always been my worst subject
Jhannybean
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It'll get better with practice :) Practice makes people perfect in math ^_^
Tabbiejack
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I remember hearing that when I was young
Tabbiejack
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I have another quesiton if you are up to it?
Jhannybean
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Of course :) Math is a lot about understanding a problem as a whole and finding a relation to a technique method in solving, it's all patterns.
Jhannybean
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sure thing
Tabbiejack
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I have 2 test to give to my children for the summer to help them prepare for summer school that is why I am getting the answers so I will be able to help them
Jhannybean
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Interesting
Tabbiejack
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What is the simplified form of the expression?|dw:1369541274406:dw|
Jhannybean
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\[\large (3x ^{\color{forestgreen}{7/2}})^{\color{blue}{6}}(x ^{\color{green}{2}})^{\color{blue}{6}}\] here, we will start 1 part at a time. lets start with \(\large (3x ^{7/2})^{6}\)
Tabbiejack
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ok what do we do next
Jhannybean
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we're going to multiply 6 to the 3 AND the x^(7/2)
Jhannybean
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Are you able to do that?
Tabbiejack
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18 x
Tabbiejack
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I suck
Jhannybean
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Hm.. not exactly, we have \[\large(3^{\color{blue}{6}})(x ^{\color{blue}{(7/2)(6)}})\] which gives us \[\large(729x ^{21})\]
Tabbiejack
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A. 729x33
B. 3x33
C. 729x29
D. 3x29
Jhannybean
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Now that we've taken care of the first part, we can move onto the second part, which is \[\large (x ^{2})^{6} = x ^{\color{red}{6*2}}= x ^{\color{blue}{12}}\]
Tabbiejack
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ok
Jhannybean
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Now we can combine both parts together so we get \[\large (729x {^\color{green}{21}}) *(x ^{\color{green}{12}}) = 729x ^{\color{red}{21+12}}\]
Jhannybean
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And adding 21 + 12 for the exponent, you'll get your answer. i've done the rest
Jhannybean
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Good luck with your other problems!
Tabbiejack
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33
Tabbiejack
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729x^33
Tabbiejack
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am I right?
Tabbiejack
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thanks so much