The nth term of a linear sequence

Objective. Find a rule for the nth term of an arithmetic sequence.

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2. Worked example
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Learn: the key idea

The common difference is the coefficient of n. Compare the multiples of that difference with the sequence to find the constant.

Worked example

Find the nth term of 5, 8, 11, 14, …

1 $Common difference is 3, so start with 3n.$
2 $3n gives 3, 6, 9, 12 — each is 2 less than the sequence.$

Answer: 3n + 2

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