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The first five terms of an arithmetic sequence are 1 4 7 10 13 Write down an expression, in terms of n, for the nth term of this sequence. - Edexcel - GCSE Maths - Question 2 - 2020 - Paper 1

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The first five terms of an arithmetic sequence are 1 4 7 10 13 Write down an expression, in terms of n, for the nth term of this sequence.

Worked Solution & Example Answer:The first five terms of an arithmetic sequence are 1 4 7 10 13 Write down an expression, in terms of n, for the nth term of this sequence. - Edexcel - GCSE Maths - Question 2 - 2020 - Paper 1

Step 1

Write down the formula for the nth term of an arithmetic sequence

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Answer

In an arithmetic sequence, the nth term can be calculated using the formula:

an=a+(n−1)da_n = a + (n-1)d

where:

  • aa is the first term of the sequence.
  • dd is the common difference between the terms.

Step 2

Identify the first term and common difference

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Answer

From the given sequence (1, 4, 7, 10, 13):

  • The first term a=1a = 1.
  • The common difference d=4−1=3d = 4 - 1 = 3.

Step 3

Substitute the values into the formula

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Answer

Substituting aa and dd into the nth term formula gives:

an=1+(n−1)3a_n = 1 + (n-1)3

This simplifies to:

an=1+3n−3=3n−2a_n = 1 + 3n - 3 = 3n - 2

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