Determine whether each sequence is arithmetic geometric or neither if the sequence is arithmetic give the common difference if geometric give the common ratio 1. 6,18,54,162, 2. 4,10,16,22 3. 1,1,2,3,5,8 4. 625,125,25,5 5. 5,8,13,21,34
1.
6 , 18 , 54 , 162
Geometric sequence. Common ratio 3
2.
4 , 10 , 16 , 22
Arithmetic sequence. Common difference 6
3.
1 ,1 , 2 , 3 , 5 , 8
Neither, Fibonacci sequence:
1 + 1 = 2 , 1 + 2 = 3 , 2 + 3 = 5 , 3 + 5 = 8
4.
625 , 125 , 25 , 5
Geometric sequence. Common ratio 1 / 5
5.
5 , 8 , 13 , 21 , 34
Neither, Fibonacci sequence:
5 + 8 = 13 , 8 + 13 = 21 , 13 + 21 = 34
arithmetic sequence, a geometric sequence, or neither. 1, 2, -1, 3, -2, ...
1. This sequence is geometric because each term is obtained by multiplying the previous term by 3. The common ratio is 3.
2. This sequence is neither arithmetic nor geometric. The differences between consecutive terms are not constant, and there is no common ratio between terms.
3. This sequence is neither arithmetic nor geometric. The differences between consecutive terms are not constant, and there is no common ratio between terms.
4. This sequence is geometric because each term is obtained by dividing the previous term by 5. The common ratio is 1/5.
5. This sequence is neither arithmetic nor geometric. The differences between consecutive terms are not constant, and there is no common ratio between terms.
To determine whether each sequence is arithmetic, geometric, or neither, we need to analyze the pattern of the terms in each sequence.
1. 6, 18, 54, 162
This sequence is a geometric sequence because each term is obtained by multiplying the previous term by the same factor, which is 3 in this case. The common ratio is 3.
2. 4, 10, 16, 22
This sequence is arithmetic because there is a common difference between each term. To find the common difference, we can subtract consecutive terms and check if they are the same. Here, the common difference is 6.
3. 1, 1, 2, 3, 5, 8
This sequence is neither arithmetic nor geometric because there is no constant difference or ratio between consecutive terms. The sequence appears to be a series of numbers following the Fibonacci sequence, where each term is the sum of the two preceding terms.
4. 625, 125, 25, 5
This sequence is also a geometric sequence because each term is obtained by dividing the previous term by the same factor, which is 5 in this case. The common ratio is 1/5.
5. 5, 8, 13, 21, 34
This sequence is neither arithmetic nor geometric because there is no constant difference or ratio between consecutive terms. However, it is worth noting that the numbers in this sequence are related to the Fibonacci sequence, where each term is the sum of the two preceding terms.