I was just wondering, what is the difference between an arithmetic sequence and a geometric sequence?
http://www.mathsisfun.com/algebra/sequences-series.html
Arithmetic sequences are the continuous adding of some constant k; which looks like a, a+k, a+2k, a+3k, etc.
Geometric sequences are the continuous multiplication by a constant, which looks like:
a, ak, ak^2, ak^3, etc.
MAG MAHAL.
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is always the same. For example, 2, 5, 8, 11, 14 is an arithmetic sequence with a common difference of 3. To find a term in an arithmetic sequence, you can use the formula:
nth term = a + (n-1)d
where a is the first term, n is the position of the term, and d is the common difference.
A geometric sequence, on the other hand, is a sequence of numbers in which each term is found by multiplying the previous term by a constant ratio. For example, 2, 6, 18, 54, 162 is a geometric sequence with a common ratio of 3. To find a term in a geometric sequence, you can use the formula:
nth term = ar^(n-1)
where a is the first term, r is the common ratio, and n is the position of the term.
The main difference between them is that in an arithmetic sequence, the difference between consecutive terms is constant, while in a geometric sequence, the ratio between consecutive terms is constant.