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2 (a) Write the next term in each of these sequences - OCR - GCSE Maths - Question 2 - 2017 - Paper 1
Question 2
2 (a) Write the next term in each of these sequences. (i) 1 1 2 3 5 8 (ii) 2 4 8 16 32 64 (b) Write an expression for the nth term of the sequence below. ... show full transcript
Worked Solution & Example Answer:2 (a) Write the next term in each of these sequences - OCR - GCSE Maths - Question 2 - 2017 - Paper 1
Step 1
(a)(i) Write the next term in the sequence 1 1 2 3 5 8
Answer
This sequence appears to follow the Fibonacci pattern where each term is the sum of the two preceding terms. Therefore:
- 1 (first term) + 1 (second term) = 2
- 1 (second term) + 2 (third term) = 3
- 2 (third term) + 3 (fourth term) = 5
- 3 (fourth term) + 5 (fifth term) = 8
Thus, to find the next term (the sixth term) in the sequence:
- 5 (fifth term) + 8 (sixth term) = 13
The next term is 13.
Step 2
(a)(ii) Write the next term in the sequence 2 4 8 16 32 64
Answer
This sequence is a geometric progression, where each term is multiplied by 2 to get the next term:
- 2 x 2 = 4
- 4 x 2 = 8
- 8 x 2 = 16
- 16 x 2 = 32
- 32 x 2 = 64
To find the next term (the sixth term):
- 64 x 2 = 128
The next term is 128.
Step 3
(b) Write an expression for the nth term of the sequence 15 12 9 6
Answer
Here, the series is decreasing by 3 with each sequential term. The first term is 15, leading to the general form for the nth term of an arithmetic sequence:
- The common difference (d) is -3,
- The first term (a) is 15.
The nth term (T_n) can be expressed as:
Substituting the known values:
Simplifying:
Thus, the expression for the nth term is 18 - 3n.