Answers

2016-07-04T22:50:37+08:00
The trick in geometric sequences is in figuring out what's called the "common ratio" or that number which keeps multiplying itself to the terms of the sequence to get the next terms.
This can be acquired by dividing a term in the sequence by a previous term, for instance, dividing 12 (the second term) by 24 (the first), and we get \frac12, which is the common ratio.

If we know the first term of a geometric sequence, and the common ratio, it is simple enough to arrive at any nth term. Simply use the following formula:
a_n = a_1\times r^{n-1} where a_n is the nth term we are looking for.

In this case, to get the eighth term, we use the formula, it gives us a_8 = 24\left(\frac12\right)^7 = 24\left(\frac1{128}\right)=\frac3{16}
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