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baherus [9]
3 years ago
10

What is 242 - 198 subtract​

Mathematics
1 answer:
kirza4 [7]3 years ago
7 0
The answer would be 44
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Find the values of t_1 and are for a geometric sequence with t_6= 4 and t_10 = 324.<br><br>​
sleet_krkn [62]
<h3>Answer: Choice C</h3>

t_1 = \frac{4}{243}, \ r = 3

==============================================

Work Shown:

Start with t_6 = 4 and multiply by the common ratio r to get the next term t_7. Keep this going until you get to the 10th term t_{10}

So we have...

t_6 = 4\\\\t_7= r*t_6 = 4r\\\\t_8 = r*t_7 = r*(r*t_6) = r^2*t_6 = 4r^2\\\\t_9 = r*t_8 = r*(r^2*t_6) = r^3*t_6 = 4r^3\\\\t_{10} = r*t_9 = r*(r^3*t_6) = r^4*t_6 = 4r^4 = 324\\

From that we can see,

4r^4 = 324\\\\r^4 = \frac{324}{4}\\\\r^4 = 81\\\\r = 81^{1/4}\\\\r = 3

At this point, the only possible answer is choice C since this is the only answer choice with r = 3 in it. We could stop here if we wanted.

For the sake of completeness, let's find t_1

t_n = t_1*(r)^{n-1}\\\\t_{6} = t_1*(3)^{6-1}\\\\4 = t_1*(3)^{5}\\\\4 = t_1*243\\\\t_1 = \frac{4}{243}

You can use t_{10} = 324 in place of t_6 = 4 in the section above, so either value is optional.

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