So, this "kiddo" needs some help plz!
You are having a discussion about sequences with your classmate. She insists that the sequence is 2, 3, 5, 8, and 12 must be either arithmetic or geometric. Is she correct. Explain.
HELP I DO NOT UNDERSTAND THIS!!!!! D;
Each number increases by one more than the preceding interval.
2 + 1 = 3
3 + 2 = 5
5 + 3 = 8
8 + 4 = 12
3 = 2*1.5
5 = 3 *1.666666 .....
1.5 is not 1.6666..
so it is not geometric
3-2 = 1
5-3 = 2 so it is not arithmetic
She's incorrect. 2,3,5,8,and 12 is not arithmetic because there is no formula. (add two repeatedly) It cannot be geometric either and we know that because most geometric sequences are things like fractions and negatives. ( -4 subtract 1 repeatedly)
That's what Damon posted.
I see the pattern it's 2+1=3,3+2=5...your adding one more then before. If that makes sense. But otherwise I'm still stumped.
Wait..it would be arithmetic right?
Don't worry, I'm here to help you understand!
In order to determine if a sequence is arithmetic or geometric, we need to understand the characteristics of each type.
An arithmetic sequence is a sequence in which the difference between any two consecutive terms is constant. For example, in the sequence 2, 5, 8, 11, the difference between each term is 3.
A geometric sequence is a sequence in which each term is obtained by multiplying the previous term by a constant factor. For example, in the sequence 2, 6, 18, 54, the common ratio between each term is 3.
Now, let's analyze the given sequence: 2, 3, 5, 8, 12.
To determine if it's arithmetic, we need to check if the difference between each term is constant. Let's calculate the differences:
3 - 2 = 1
5 - 3 = 2
8 - 5 = 3
12 - 8 = 4
As you can see, the differences are not constant. So, the sequence is not arithmetic.
To determine if it's geometric, we need to check if the ratio between each term is constant. Let's calculate the ratios:
3 / 2 = 1.5
5 / 3 ≈ 1.67
8 / 5 = 1.6
12 / 8 = 1.5
Again, the ratios are not constant. So, the sequence is not geometric either.
In conclusion, your classmate is incorrect. The sequence 2, 3, 5, 8, 12 is neither arithmetic nor geometric because it does not have a constant difference or ratio between terms.