Help with this math problem please! (Don't know how to use the formula)

Test Preparation
1

<p>This is the problem, from Kaplan's SAT Math Workbook:</p>

<p>If the first term in a geometric sequence is 7, and the third term is 63, what is the ninth term?</p>

<p>(A) 367
(B) 567
(C) 2,209
(D) 45,927
(E) 165,247</p>

<p>It says to use this formula, but I don't understand it. Any help will be appreciated :)</p>

<p><a href="http://img.photobucket.com/albums/v43/Eric02/equation.gif%5B/url%5D"&gt;http://img.photobucket.com/albums/v43/Eric02/equation.gif&lt;/a&gt;&lt;/p>

2

<p>You could use the formula, but it's much quicker to use just a general understanding:
in geommetric sequence each term (except for the very first one) is calcilated by multimplying the previous one by the same constant number.
Example:
2
2<em>3=6
6</em>3=18
18<em>3=54,
54</em>3=162,
so on...
2, 6, 54, 162, ... - terms of geometric sequence.</p>

<p>If you take every 3rd term from this sequence starting from the first (on any other, for that matter), it would also be a geometric sequence:
2
18=2<em>9
162=18</em>9, ...
2, 18, 162, ...
Could you explain why?</p>

<p>In your question
the first term is 7, the third one is 63
63/7=9.
That means that the fifth one would be
63<em>9 ~ 63</em>10 =630
The seventh
630<em>9 ~ 630</em>10 = 6300
The ninth
6300<em>9 ~ 6300</em>10 = 63000.
Exact value should be less than 63000, but not by much (10-20 grand don't really matter here) - so
(D) 45,927
is the answer.</p>

<p>It seems like quite a long solution, but in reality you'd just do
3....5....7....9
63<em>10</em>10*10=63000</p>

3

<p>The answer is D. This is how you get it using the formula. a sub 1 is 7 and a sub 3 is 63<br>
plug that into the formula like this: 63=7<em>r^2
now solve for r
r^2=9
r=3
so, the common ratio (r) is 3
now, plug in that information and solve for a sub 9
a sub 9=7</em>(3^(9-1)) or</p>

<p>7*6561=45,927</p>

4

<p>Humm ...</p>

<p>So, you have a formula to find nth term of a geometric sequence where a{1} is the first term of the sequence and r is the common ratio. {} represents the subscript notation. </p>

<p>The formula would be a{n} = a{1} r^n-1</p>

<p>Let's see how the sequence looks</p>

<p>7 - 63 - - - - - - -</p>

<p>You need to be able to see the common rate, which in this case is "Multiply by 3" </p>

<p>So you have 7 21 63 - - - - - - -</p>

<p>Apply the formula and you should obtain a{9} = 7 * 3^(9-1) or 7<em>3^8 or 7</em>6561 or 45,927. </p>

<p>Of course, after having seen the common rate, you could have used your calculator to multiply 7 by 3 and hit *3 eight more times. </p>

<p>If you want to read more about sequences, read the following pages:
<a href="http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut54d_geom.htm%5B/url%5D"&gt;http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut54d_geom.htm&lt;/a&gt;&lt;/p>

5

<p>Instead of
2, 6, 54, 162, ... - terms of geometric sequence.
should be
2, 6, 18, 54, 162, ... - terms of geometric sequence.</p>

<p>Instead of
If you take every 3rd term from this sequence starting from the first (on any other, for that matter), it would also be a geometric sequence:
should be
If you take every other term from this sequence starting from the first one (or any other, for that matter), it would also be a geometric sequence:</p>

<p>Staying up late clouds the mind sometimes... (like giving feet to caterpillar when thinking of centipede's legs :o).</p>