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My Maths Cheats For Homework Nth Term Rule

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Objective: I know how to find the pattern and the nth 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 41st number, or 110th 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 nth term rule.

Question

What is the nth term of this sequence?

Answer

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

So the nth term is 5 × n or 5n

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

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

Question

What are the nth term and the 10th term of this sequence: 2, 4, 6, ... ?

Answer

nth term = 2n

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

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