2, 1,1/2 , 1/4 , . ..
arithmetic
geometric
both
neither
I don't know how to solve it?
http://www.mathsisfun.com/algebra/sequences-sums-geometric.html
I don't know how to do it with the fractions. Also that is the first website I turn to besides this one for help
Please Help Me!!
Found the answer..
Geometric
To determine whether the given sequence (2, 1, 1/2, 1/4, ...) is arithmetic, geometric, both, or neither, we need to look for certain patterns in the sequence.
An arithmetic sequence is a sequence in which the difference between any two consecutive terms is constant. To check if it is arithmetic, we subtract each term from its succeeding term and see if we get a consistent difference. Let's see:
1 - 2 = -1
1/2 - 1 = -1/2
1/4 - 1/2 = -1/4
As you can see, the differences are not constant, so the sequence is not arithmetic.
A geometric sequence is a sequence in which each term is obtained by multiplying the preceding term by a constant factor (called the common ratio). To check if it is geometric, we divide each term by its preceding term and see if we get a consistent ratio. Let's see:
1 / 2 = 1/2
(1/2) / 1 = 1/2
(1/4) / (1/2) = 1/2
The ratios are consistent in this case (1/2), so the sequence is geometric.
Since the sequence is not arithmetic but is geometric, we can say that it is a geometric sequence. Therefore, the answer is geometric.