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Here are the first four terms of a sequence - OCR - GCSE Maths - Question 26 - 2018 - Paper 1

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Question 26

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Here are the first four terms of a sequence. 28 23 18 13 Find the nth term of the sequence.

Worked Solution & Example Answer:Here are the first four terms of a sequence - OCR - GCSE Maths - Question 26 - 2018 - Paper 1

Step 1

Identify the Pattern

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Answer

The given sequence is 28, 23, 18, 13. We can observe that each term is decreasing by 5, then decreasing by 5 for each subsequent term.

  • From 28 to 23, the decrease is 5.
  • From 23 to 18, the decrease is 5.
  • From 18 to 13, the decrease is 5.

Step 2

Formulate the nth Term

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Answer

Given that the sequence decreases by 5 each time, we can express the nth term of the sequence using the formula:

an=28−5(n−1)a_n = 28 - 5(n - 1)

Here, 28 is the first term and 5 is the common difference. Simplifying this gives:

an=28−5n+5=33−5na_n = 28 - 5n + 5 = 33 - 5n

Thus, the nth term can be expressed as an=33−5na_n = 33 - 5n.

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