For each sequence, state if it us arithmetic, geometric, or neither
3) 1, 8, 15, 22, 29, ...
5) 18, 27, 36, 45, 54, ...
4) -34,-40, -46, -52, -58,...
6) 8. 12, 16, 20, 24,...
3) Arithmetic; the common difference is 7.
5) Arithmetic; the common difference is 9.
4) Arithmetic; the common difference is -6.
6) Arithmetic; the common difference is 4.
3) This sequence is arithmetic. It is increasing by 7 each time.
5) This sequence is arithmetic. It is increasing by 9 each time.
4) This sequence is arithmetic. It is decreasing by 6 each time.
6) This sequence is arithmetic. It is increasing by 4 each time.
To determine if each sequence is arithmetic, geometric, or neither, we need to look for certain patterns in the sequences.
1) 1, 8, 15, 22, 29, ...
To determine if this sequence is arithmetic, we check if there is a common difference between consecutive terms. To find the common difference, we subtract any term from the next term. Let's calculate:
8 - 1 = 7
15 - 8 = 7
22 - 15 = 7
29 - 22 = 7
Since the difference between each consecutive term is always 7, the sequence is arithmetic.
2) 18, 27, 36, 45, 54, ...
To determine if this sequence is arithmetic, we once again check if there is a common difference between consecutive terms.
27 - 18 = 9
36 - 27 = 9
45 - 36 = 9
54 - 45 = 9
Since the difference between each consecutive term is always 9, the sequence is arithmetic.
3) -34, -40, -46, -52, -58,...
To determine if this sequence is arithmetic, we check if there is a common difference between consecutive terms.
-40 - (-34) = -6
-46 - (-40) = -6
-52 - (-46) = -6
-58 - (-52) = -6
Since the difference between each consecutive term is always -6, the sequence is arithmetic.
4) 8, 12, 16, 20, 24,...
To determine if this sequence is arithmetic, we once again check if there is a common difference between consecutive terms.
12 - 8 = 4
16 - 12 = 4
20 - 16 = 4
24 - 20 = 4
Since the difference between each consecutive term is always 4, the sequence is arithmetic.
Therefore, the classification for each sequence is:
1) Arithmetic
2) Arithmetic
3) Arithmetic
4) Arithmetic