State whether the given sequence is ARITHMETIC or NOT. If it is arithmetic, give the common difference.
1. 8, 13, 21, 34, 55, ...
2. 8, 16, 24, 32, ...
3. 1/9, 1/27, 1/81, ...
4. 1296, 216, 36, 6, ...
5. %, 1, 5/4, 3/2, ...
6. 1/24, 1/20, 1/16, 1/12, ...
7. 6, -18, 54, -162, ...
8. 40, 8, 8/5, 8/25, ...
9. 11, 2, -7, -16, ...
10. 8.2, 8, 7.8, 7.6, ...
Answer (1)
To determine if the sequences are arithmetic and to find the common difference, we need to check if each term after the first is obtained by adding a fixed number to the previous term.
Sequence: 8, 13, 21, 34, 55, ...
This sequence is not arithmetic . The differences between consecutive terms (13 - 8 = 5, 21 - 13 = 8, 34 - 21 = 13, ...) are not constant.
Sequence: 8, 16, 24, 32, ...
This sequence is arithmetic . The common difference is 8 (16 - 8).
Sequence: 9 1 , 27 1 , 81 1 , ...
This sequence is not arithmetic . The differences are not constant, the sequence seems to be decreasing by multiplying by 3 1 .
Sequence: 1296, 216, 36, 6, ...
This sequence is not arithmetic . It is decreasing by dividing by 6.
Sequence: %, 1, 4 5 , 2 3 , ...
This sequence is arithmetic . The common difference is 4 1 .
Sequence: 24 1 , 20 1 , 16 1 , 12 1 , ...
This sequence is not arithmetic . The differences are not constant, as each term increases differently.
Sequence: 6, -18, 54, -162, ...
This sequence is not arithmetic . It is a geometric sequence.
Sequence: 40, 8, 5 8 , 25 8 , ...
This sequence is not arithmetic . Each term is obtained by dividing the previous one by 5.
Sequence: 11, 2, -7, -16, ...
This sequence is arithmetic . The common difference is -9 (2 - 11).
Sequence: 8.2, 8, 7.8, 7.6, ...
This sequence is arithmetic . The common difference is -0.2 (8 - 8.2).
