For each sequence, determine whether it appears to be arithmetic, geometric, or neither.
13, 10, 7,4 Arithmetic
Geometric
Neither
1600, 400,100, 25,..Arithmetic
Geometric
Neither
25,36,49,64,..Arithmetic
Geometric
Neither
check for a common difference or ratio.
#1. d = -3
#2. r = 1/4
#3. neither (quadratic)
To determine whether a sequence is arithmetic, geometric, or neither, we need to analyze the pattern of the numbers in the sequence.
For the first sequence 13, 10, 7, and 4, we can see that each number is decreasing by 3. This suggests that the sequence is arithmetic. To confirm, we can calculate the common difference between consecutive terms: 10 - 13 = -3, 7 - 10 = -3, and 4 - 7 = -3. Since the common difference is the same (-3), we can conclude that the sequence is indeed arithmetic.
For the second sequence 1600, 400, 100, and 25, we can observe that each number is decreasing by dividing by 4. This suggests that the sequence is geometric. To confirm, we can calculate the common ratio between consecutive terms: 400 / 1600 = 0.25, 100 / 400 = 0.25, and 25 / 100 = 0.25. Since the common ratio is the same (0.25), we can conclude that the sequence is geometric.
For the third sequence 25, 36, 49, and 64, there does not seem to be a consistent pattern of addition or multiplication between terms. Therefore, this sequence is neither arithmetic nor geometric.
In summary:
Sequence 1: Arithmetic
Sequence 2: Geometric
Sequence 3: Neither