Determine whether each sequence is arithmetic of geometric. Find the next three terms.
14,19,24,29....
A. Geometric,34,39,44
B. Arithmetic,32,36,41
C. Arithmetic, 34,39,44
D. This sequence is neither arithmetic or geometric.
Is the answer C?
Thank you
In an Arithmetic Sequence the difference between one term and the next is a constant.
19 - 14 = 5
24 - 19 = 5
29 - 24 = 5
So difference = 5
29 + 5 = 34
34 + 5 = 39
39 + 5 = 44
Answer A
But a geometric sequence is when you times it and arithmetic is when you add it. So the answer has to be C, because C answer and A's answer are the same except arithmetic is the right answer.
The answer is C. The common difference between all the terms and the theorized next three terms is 5.
To determine whether a sequence is arithmetic or geometric, we need to check if there is a constant difference between consecutive terms (for arithmetic) or a constant ratio (for geometric).
Let's examine the given sequence: 14, 19, 24, 29.
To determine if it is an arithmetic sequence, we need to check if there is a constant difference between consecutive terms. To do this, we subtract each term from its previous term:
19 - 14 = 5
24 - 19 = 5
29 - 24 = 5
Since the differences are constant (5 in this case), we can conclude that the sequence is arithmetic.
Now that we know the sequence is arithmetic, we can find the next terms by adding the constant difference to the last term in the sequence:
29 + 5 = 34
34 + 5 = 39
39 + 5 = 44
So, the next three terms in the arithmetic sequence are 34, 39, and 44.
Based on this analysis, the correct answer is C.