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![geometric sequences geometric sequences](https://i.ytimg.com/vi/3d-X_v4wHmc/maxresdefault.jpg)
GEOMETRIC SEQUENCES SERIES
Since the sum of the geometric series is $18$ and $r \neq 1$, An arithmetic sequence is a sequence with. Thus, if we divide equation 2 by equation 1, we obtain Some sequences are arithmetic or geometric, meaning they either change by some common difference or common ratio. Moreover, the terms of the arithmetic sequence must be distinct, so $d \neq 0$. Since the terms of the geometric sequence are all different, $a_1 \neq 0$ and $r \neq 1$. Since the second term of the geometric sequence is equal to the eleventh term of the arithmetic sequence, equality is preserved if we subtract the second term of the geometric sequence from the left-hand side and the eleventh term of the arithmetic sequence from the right-hand side, which yieldsĪ_1r^2 - a_1r & = a_1 + 15d - (a_1 + 10d)\\
![geometric sequences geometric sequences](https://i.ytimg.com/vi/eiDrKxkMZOY/maxresdefault.jpg)
The common ratio can be found by dividing any term in the sequence by the previous term. This constant is called the common ratio of the sequence. Since the third term of the geometric sequence is equal to the sixteenth term of the geometric sequence, Definition: GEOMETRIC SEQUENCE A geometric sequence is one in which any term divided by the previous term is a constant. Subtracting the first term of the sequence from each side gives Since the second term of the geometric sequence is the eleventh term of the arithmetic sequence, You will also discern the difference between an arithmetic sequence and a geometric sequence. I will use $a_1$ for the initial term of both sequences, $r$ for the common ratio of the geometric sequence, and $d$ for the common difference.
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