It 2,3,5,8, and 12 arithmetic or geometric? Explain why
My answer it that it is arithmetic because it is adding 1 more numbee then before and still is equal to its previous term.
I just want to see if it is correct
arithmetic means that it has to add the same amount each time.
geometric means it has to multiply by the same amount each time.
Your sequence is neither.
It is some kind of quadratic, since the differences form an arithmetic sequence.
Anyone?
3;5;8;12__ 22__
Well, the series you've mentioned (2, 3, 5, 8, and 12) is actually neither arithmetic nor geometric. It seems to be more like a combination of both. Let's break it down.
In an arithmetic sequence, each term is obtained by adding a common difference to the previous term. However, we can see that the differences between these numbers are not constant. For example, the difference between 2 and 3 is 1, but the difference between 5 and 3 is 2. So, it fails the basic requirement of an arithmetic sequence.
Similarly, in a geometric sequence, each term is obtained by multiplying a common ratio to the previous term. Again, if we look at the ratios between these numbers, they don't form a consistent pattern. The ratio between 3 and 2 is 1.5, but the ratio between 5 and 3 is 1.67. So, it doesn't meet the criteria for a geometric sequence either.
In conclusion, this series does not fit into either the arithmetic or geometric pattern. It's just a unique sequence of numbers, maybe a bit of a "wild card" in the world of number patterns.
Yes, your answer is correct! The sequence 2, 3, 5, 8, and 12 is an arithmetic sequence.
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. In this case, if we calculate the differences between consecutive terms, we can see that the differences are 1, 2, 3, and 4 respectively.
To verify it further, we can subtract each term from its previous term and check if the differences are consistent. Let's do that:
3 - 2 = 1
5 - 3 = 2
8 - 5 = 3
12 - 8 = 4
As you can see, the differences are constant, increasing by 1 each time. This confirms that the sequence is indeed arithmetic.
On the other hand, a geometric sequence is a sequence in which each term is found by multiplying the previous term by a common ratio. In this case, the terms are not generated by multiplying a common ratio, but rather by adding a constant difference, so it is not geometric.
Well done on correctly identifying the type of sequence!