Find the next three terms in each geometric sequence.
The next three terms in the geometric sequence are .
In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3.
The ration of term and first term is called the common ratio.
Each term in a geometric sequence can be expressed in terms of the first term and the common ratio . Since each succeeding term is formulated from one or more previous terms, this is a recursive formula.
First term and the common ratio is:
In order to calculate the next three terms of the geometric sequence substitute and for into the formula .
In terms of and
Thus, next three terms of the sequence are .
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