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Q3 (a) Fill in the boxes to make this a linear pattern - Junior Cycle Mathematics - Question 3 - 2018
Question 3
Q3 (a) Fill in the boxes to make this a linear pattern. 10 14 (b) Fill in the boxes to make this a quadratic pattern. 2 4 7
Worked Solution & Example Answer:Q3 (a) Fill in the boxes to make this a linear pattern - Junior Cycle Mathematics - Question 3 - 2018
Step 1
Fill in the boxes to make this a linear pattern.
Answer
To find the missing numbers in the linear pattern, we first identify the increments between the known numbers.
We see that:
- The difference between 10 and 14 is 4.
Using the linear sequence formula, we can define the pattern. Let the first term be 10, then:
- First box: 10 - 4 = 6
- Second box: 10 + 4 = 14
- Therefore, the complete sequence is 6, 10, 14, 18, 22.
Thus, the numbers to fill in are 6, 18, and 22.
Step 2
Fill in the boxes to make this a quadratic pattern.
Answer
To fill in the boxes to complete the quadratic pattern, we need to find the second differences. The known terms are:
- 2, 4, 7
First, we find the first differences:
- Between 2 and 4: 4 - 2 = 2
- Between 4 and 7: 7 - 4 = 3
Next, we find the second differences:
- Second difference between 2 and 3 = 3 - 2 = 1.
As the second difference is constant, we can conclude that the next first difference would increase by 1. Thus:
- New first difference: 3 + 1 = 4.
- Adding this to the last known term (7), we find: 7 + 4 = 11.
Following this method, the complete quadratic sequence is 2, 4, 7, 11, 16.