geometric sequence
a sequence in which each term is found by multiplying the previous term by the same numbers
A geometric sequence, also known as a geometric progression, is a sequence of numbers in which each term after the first is obtained by multiplying the preceding term by a fixed non-zero number called the common ratio.
For example, the sequence 2, 4, 8, 16, 32, … is a geometric sequence because each term is obtained by multiplying the preceding term by 2.
The general formula for a geometric sequence is:
a, ar, ar^2, ar^3, ar^4, …
where
a = the first term in the sequence
r = the common ratio
To find any term in a geometric sequence, you can use the formula:
tn = a*r^(n-1)
where
tn = the nth term in the sequence
a = the first term in the sequence
r = the common ratio
n = the term number
A geometric sequence can also be finite or infinite. A finite geometric sequence has a fixed number of terms, while an infinite geometric sequence continues indefinitely.
Some examples of real-life applications of geometric sequences include population growth, compound interest, and the growth of certain plant species.
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