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In a particular linear sequence, the second term is 40 and the sixth term is 116 - Junior Cycle Mathematics - Question 11 - 2017
Question 11
In a particular linear sequence, the second term is 40 and the sixth term is 116. Fill in the boxes below to show the rest of the first six terms of this sequence. ... show full transcript
Worked Solution & Example Answer:In a particular linear sequence, the second term is 40 and the sixth term is 116 - Junior Cycle Mathematics - Question 11 - 2017
Step 1
Find the missing terms in the linear sequence
Answer
To find the first and third terms of the linear sequence, we first determine the common difference (d).
Since the second term is 40 and the sixth term is 116, we can find d using:
Solving for d:
Now we can find the first and third terms:
- First term: 40 - 19 = 21
- Third term: 40 + 19 = 59
Thus, the first six terms of the sequence are:
- 21, 40, 59, 78, 97, 116
Step 2
Identify the incorrect term in Orla's quadratic sequence
Answer
To analyze Orla's sequence:
5, 6, 9, 14, 22, 30, 41
1st differences:
- 6 - 5 = 1
- 9 - 6 = 3
- 14 - 9 = 5
- 22 - 14 = 8
- 30 - 22 = 8
- 41 - 30 = 11
Thus, the first differences are: 1, 3, 5, 8, 8, 11
Next, we find the 2nd differences:
- 3 - 1 = 2
- 5 - 3 = 2
- 8 - 5 = 3
- 8 - 8 = 0
- 11 - 8 = 3
Thus, the second differences are not constant, indicating an error in the quadratic sequence.
The corrected quadratic sequence is: 5, 6, 9, 14, 21, 30, 41
We change 22 to 21.