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The next term in each of these Fibonacci sequences is found by adding together the two previous terms - OCR - GCSE Maths - Question 14 - 2018 - Paper 2
Question 14
The next term in each of these Fibonacci sequences is found by adding together the two previous terms. Work out the missing terms in each sequence. (a) 2 5 7 12 ... show full transcript
Worked Solution & Example Answer:The next term in each of these Fibonacci sequences is found by adding together the two previous terms - OCR - GCSE Maths - Question 14 - 2018 - Paper 2
Step 1
(a) 2 5 7 12 .......... ..........
Answer
To find the missing terms in the sequence, we follow the Fibonacci rule where each term is the sum of the two preceding terms.
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Start with the given series: 2, 5, 7, 12.
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The next term after 12 is calculated as follows:
12 + 7 = 19
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Continuing, the term after 19 is:
19 + 12 = 31
Therefore, the missing terms are 19 and 31.
Step 2
(b) .......... .......... 22 34
Answer
For part (b), we approach the sequence from the known values: 22 and 34.
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To find the term before 22, we note that:
22 + x = 34
Solving this, we find:
x = 34 - 22 = 12
Thus, the term before 22 is 12.
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Now, finding the term before 12 involves:
12 + y = 22
Solving this gives:
y = 22 - 12 = 10
Therefore, the missing terms are 10 and 12.