Sequences and nth term worksheet

Master sequences and nth terms with this structured worksheet. Students progress through three stages: first substituting values into nth terms to generate sequences, then finding nth terms themselves and finally solving more challenging problems.

What's included

• Clear structure with 6 distinct sections, from generating sequences to complex problem-solving
• Varied question types including generating sequences, finding terms and nth term calculations
• Full answer key included for easy marking and self-assessment

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How to use this nth term worksheet

Designed for upper KS3 and KS4 students, this resource works brilliantly as a complete lesson activity or for homework. The progression from basic concepts to more challenging problems allows for differentiation and builds students’ confidence. Start with guided practice on the earlier questions before letting students tackle the more complex questions independently.

Looking for more like this?

Browse more sequences and nth term resources, or try:

• nth term of a linear sequence
• Finding the nth term of a quadratic sequence
• nth term mixture worksheet

Questions in this nth term worksheet

1. Write the first 6 terms of each sequence.

2. For each of the sequences in question 1 find the value of term 10 and term 50.

Part (a) has been done as an example.

a. 2n + 1            Term 10 = 20 + 1 = 21

Term 50 = 100 + 1 = 101                

3. Find the nth term for each of these sequences, then find the value of term 20.

4. You are given the term to term rule for each sequence and the value of the third term.

Work out the first term.

a. Multiply the previous term by 2 then subtract 3

Third term = 27                  

b. Multiply the previous term by 2 then add 4

Third term = 32                  

c. Multiply the previous term by 3 then subtract 1

Third term = 59                  

d. Add 4 to the previous term then multiply by 2

Third term = 36                  

5. 

a. Find which term in the sequence  3n + 1 has the value 76.

b. Find which term in the sequence  2n - 5 has the value 31.

c. Find which term in the sequence  4n - 2 has the value 82.

6. 

a. Is 37 a term in the sequence 4n - 1?

b. Is 71 a term in the sequence 2n + 3?

c. Is 60 a term in the sequence 5n + 4?

d. Is 40 a term in the sequence 3n - 5?

e. Which is the first term greater than 100 in the sequence 6n - 5?