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Year 8
Sequences & the Nth Term
Definition
A sequence is a list of numbers that follows a rule. The nth term is a formula that gives any term straight away: for 3, 7, 11, 15 the rule is 4n − 1, so the 100th term is 399 without counting up.
Why Do I Have to Learn This?
Sequences are number patterns that follow a rule. Spotting the rule lets you predict what comes next.
Key Rules:
- 1. Find the common difference first: it becomes the number in front of n.
- 2. Then adjust: compare difference × 1 with the first term to find what to add or subtract.
- 3. Test the formula on the first three terms before trusting it.
Remember:
- •Common slip: writing n + 4 for a sequence that goes up in 4s, it should be 4n plus or minus something.
- •n counts the position (1st, 2nd, 3rd…), it is not the term itself.
- •Sequences can go down: a negative difference means a negative n coefficient.
nth term
A rule for finding any term in a sequence from its position, n. For a sequence going up in equal steps of d, nth term = dn + (first term − d).
For 5, 7, 9, 11 the nth term is 2n + 3, so the 10th term is 23.
Animated Example:
3
→×2
→+1
→7
3 → ×2 → +1 → 7
Free Sequences & the Nth Term Worksheet
Download free worksheets and practise today.
Every download has a fresh set of questions.
Let’s Practise the Concept
Step 1 of 3
Put them in order
Tap the numbers from smallest to largest.
In order so far: nothing yet