Match the sequence (term) with the correct type of sequence (definition).
Match Term Definition
128, 32, 8, 2, ... A) Geometric, common ratio is 0.25
1, 3, 9, 27, ... B) Arithmetic, common difference is 5
5, 10, 15, 20, ... C) Geometric, common ratio is 3
20, 17, 14, 11, ... D) Arithmetic, common difference is -3
1A
2C
3B
4D
1b
2c
3a
4d
To match the sequence with the correct type of sequence, you need to understand the definitions of arithmetic and geometric sequences and identify the common difference or common ratio.
Arithmetic Sequence: In an arithmetic sequence, each term is obtained by adding a constant value to the previous term. This constant value is called the common difference.
Geometric Sequence: In a geometric sequence, each term is obtained by multiplying the previous term by a constant value called the common ratio.
Let's analyze each sequence and match them with the correct type:
A) 128, 32, 8, 2, ...
To determine if this sequence is arithmetic or geometric, we can calculate the common ratio by dividing any term by its previous term. For example, 32/128 = 0.25, 8/32 = 0.25, 2/8 = 0.25. Since the common ratio is 0.25, the sequence is a geometric sequence.
B) 1, 3, 9, 27, ...
Similarly, let's calculate the common difference by subtracting any term from its previous term. The differences between terms are: 3 - 1 = 2, 9 - 3 = 6, 27 - 9 = 18. As the common difference is not constant, this sequence is not arithmetic.
C) 5, 10, 15, 20, ...
To check if this sequence is arithmetic, let's calculate the common difference: 10 - 5 = 5, 15 - 10 = 5, 20 - 15 = 5. The common difference is 5, so this sequence is arithmetic.
D) 20, 17, 14, 11, ...
Finally, let's determine the common difference for this sequence: 17 - 20 = -3, 14 - 17 = -3, 11 - 14 = -3. The common difference is -3, indicating an arithmetic sequence.
Now, we can match the sequences with their type:
A) Geometric, common ratio is 0.25
B) Not an arithmetic sequence
C) Arithmetic, common difference is 5
D) Arithmetic, common difference is -3
1 B
2 d
3 a
4c