A geometric sequence is kind of like a arithmetic sequence, only that the operation isn’t either addition or subtraction, you have multiplication or division. That’s really all there is. An example would be: 2, 4, 8, 16, 32, 64,… . As you can see, each succeeding term is multiplied by 2.
You can find the constant, or the number by which the geometric sequence is being multiplied by, is by taking two succeeding numbers, like 32 and 16, and dividing the one that came after by the one that came before it. So in this case, we’d divide 32 by 16, and we’d get that the constant is 2.
The common ratio, or the constant, is called “r,” and the equation for finding it is: (an+ 1)÷ an. The n+ 1 part just represents the next number in the sequence. There is also a formula for finding the next number in the sequence, which is an × r. The formula for finding any number in the sequence is a1 × rn – 1. So for example, if we’re trying to find the 30th number in the sequence in the first paragraph, we can say that an = 2 × 229 = 1, 073, 741, 824. As you can see, these numbers get pretty large, pretty quick!
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