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Here are the first four terms of a sequence - OCR - GCSE Maths - Question 14 - 2021 - Paper 1
Question 14
Here are the first four terms of a sequence. 8 15 22 29 (i) Write down the next term in the sequence. (ii) Explain how you worked out your answer. (b) The nth... show full transcript
Worked Solution & Example Answer:Here are the first four terms of a sequence - OCR - GCSE Maths - Question 14 - 2021 - Paper 1
Step 1
(a)(i) Write down the next term in the sequence.
Answer
To find the next term in the sequence, we first identify the pattern in the given terms: 8, 15, 22, 29.
Calculating the differences between consecutive terms gives:
- From 8 to 15:
- From 15 to 22:
- From 22 to 29:
Since the difference is consistent at 7, we can determine the next term by adding 7 to the last term:
Thus, the next term is 36.
Step 2
(a)(ii) Explain how you worked out your answer.
Answer
I worked out my answer by first calculating the differences between the consecutive terms of the sequence. Each difference was found to be 7, indicating a linear pattern consistent throughout the sequence. By adding this common difference of 7 to the last term (29), I deduced that the next term must be 36.
Step 3
(b) Explain why 32 is not a term in this sequence.
Answer
In the sequence defined by the formula , we can determine the terms by substituting integer values for . Let's check what values of correspond to the term 32:
Setting the equation leads to:
Since must be a whole number (as it represents the position in the sequence), 32 cannot be obtained from this formula, and thus, it is not a term in the sequence.