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Only one linear pattern begins with "1, 7" - Junior Cycle Mathematics - Question 1 - 2018
Question 1
Only one linear pattern begins with "1, 7". Fill in the three boxes below so that the numbers form this linear pattern. Linear pattern: 1, 7, ___, ___, ___ Many di... show full transcript
Worked Solution & Example Answer:Only one linear pattern begins with "1, 7" - Junior Cycle Mathematics - Question 1 - 2018
Step 1
Fill in the three boxes below so that the numbers form this linear pattern.
Answer
To identify the linear pattern, we first determine the common difference. Starting with the numbers 1 and 7:
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Calculate the First Difference: The first difference is calculated as follows:
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Identify the Next Terms: To find the next terms in the pattern, we continue adding the first difference (6).
- The term after 7 is:
- The term after 13 is:
- The term after 19 is:
So the completed linear pattern is: 1, 7, 13, 19, 25.
Step 2
Fill in the three boxes below so that the numbers form a quadratic pattern.
Answer
For the quadratic pattern, we start again with the initial two numbers: 1 and 7.
- Determine the Second Differences:
- Let's assume the next term is 14, so we have:
- First differences: 7 - 1 = 6 14 - 7 = 7
- The second difference gives us:
- For the next term, continuing this pattern, let's assume:
- The next differences should vary to yield a different total: 22 - 14 = 8; the next second difference will yield:
- Let's assume the next term is 14, so we have:
Therefore, one possible completed quadratic pattern is: 1, 7, 14, 22, 32, demonstrating that the second difference remains constant.