AM I ARITHMETIC OR NOT? Identify whether the given sequence is arithmetic or not. Write AS if is an arithmetic sequence, otherwise, write NA. Write the solution of each question.
Hint: For item number 1 , the succeeding terms are obtained by adding the common difference, 6 , to the preceding terms. Therefore, it is an arithmetic seauence.
_____1. 5, 11, 17, 23, ...
_____2. 3, 9, 27, 81, ...
_____3. 12, 9, 6, 3, ...
_____4. 1, 1/2, 1/3, 1/4, ...
_____5. 8, 17/2, 9, 19/2, ...
How were you able to identify if the sequence is arithmetic or not? If some of the examples above are not arithmetic, what kind of sequence are they?
Let's discover another type of sequence through this module.
Hint: For item number 1 , the succeeding terms are obtained by adding the common difference, 6 , to the preceding terms. Therefore, it is an arithmetic seauence.
_____1. 5, 11, 17, 23, ...
_____2. 3, 9, 27, 81, ...
_____3. 12, 9, 6, 3, ...
_____4. 1, 1/2, 1/3, 1/4, ...
_____5. 8, 17/2, 9, 19/2, ...
How were you able to identify if the sequence is arithmetic or not? If some of the examples above are not arithmetic, what kind of sequence are they?
Let's discover another type of sequence through this module.
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Answer:
1. AS
2. NA
3. AS
4. NA
5. AS
Step-by-step explanation:
Let's solve each sequence:
1. 5, 11, 17, 23, ...
Common difference: 11 - 5 = 6
Yes, each term is obtained by adding 6 to the preceding term.
Solution: **AS (Arithmetic Sequence)**
2. 3, 9, 27, 81, ...
The terms here are not obtained by adding a common difference but by multiplying by 3.
Solution: **NA (Not Arithmetic)**
3. 12, 9, 6, 3, ...
Common difference: 9 - 12 = -3
Yes, each term is obtained by subtracting 3 from the preceding term.
Solution: **AS (Arithmetic Sequence)**
4. 1, 1/2, 1/3, 1/4, ...
The terms are not obtained by adding or subtracting a common difference. Instead, the terms are reciprocals of natural numbers.
Solution: **NA (Not Arithmetic)**
5. 8, 17/2, 9, 19/2, ...
Let's convert the terms into a common format:
8 = 16/2
17/2
9 = 18/2
19/2
Common difference: 17/2 - 16/2 = 1/2
Yes, each term is obtained by adding 1/2 to the preceding term.
Solution: AS (Arithmetic Sequence)