Is a number in a sequence?

Objective. Use an nth-term rule to test sequence membership.

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2. Worked example
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Learn: the key idea

Testing term membership means deciding whether a given number appears somewhere in a sequence by using its nth-term rule. Set the rule equal to the target number, solve for n, and check whether n comes out as a positive whole number. For the rule 4n + 1, checking whether 37 is a term means solving 4n + 1 = 37, giving n = 9, which is a whole number, so 37 is the 9th term. If n is not a whole number, the value is not in the sequence.

Worked example

Is 58 a term of the sequence with nth term 5n + 3?

1 $Set the rule equal to 58: 5n + 3 = 58$
2 $Subtract 3 from both sides: 5n = 55$
3 $Divide both sides by 5: n = 11$
4 $Since n is a whole number, 58 is a term (the 11th term)$

Answer: Yes, 58 is the 11th term

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Common mistake. Pupils often stop once they find a value of n without checking it is a whole number, wrongly accepting 50 as a term of 4n + 1 even though n = 12.25. Always confirm n is a positive integer before confirming membership.

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