## My Maths Cheats For Homework Nth Term Rule

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Objective: I know how to find the pattern and the n

^{th}term of a sequence.

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## Finding the nth term

Sometimes, rather than finding the next number in a linear sequence, you want to find the 41^{st} number, or 110^{th} number, say.

Writing out 41 or 110 numbers takes a long time, so you can use a general rule.

To find the value of any term in a sequence, use the n^{th} term rule.

- Question
What is the n

^{th}term of this sequence?

- Answer
1st = 5 (5 × 1); 2nd = 10 (5 × 2); 3rd = 15 (5 × 3)

So the n

^{th}term is 5 × n or 5n

For example, to find the 10^{th} term, work out 5 × 10 = 50. To find the 7^{th} term, work out 5 × 7 = 35

So the 41^{st} term is 5 × 41 = 205 and the 110^{th} term is 5 × 110 = 550

- Question
What are the n

^{th}term and the 10^{th}term of this sequence: 2, 4, 6, ... ?

- Answer
n

^{th}term = 2n10

^{th}term = 20. To work this out, n = 10, so 2n = 2 × 10 = 20

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