Sequences (Nth Term) - Worksheets, Questions and Revision

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GCSE · Algebra

4.7 Sequences (Nth Term)

EDEXCEL 1MA1 · Calculator allowed · about 75 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Here are the first four terms of a sequence.
3, 7, 11, 15
(a)Write down the next term of the sequence.(1)
(b)Describe, in words, the term-to-term rule for the sequence.(1)
(Total for Question 1 is 2 marks)
2
Here are the first four terms of a sequence.
3, 6, 12, 24
(a)Write down the next term of the sequence.(1)
(b)Describe, in words, the term-to-term rule for the sequence.(1)
(Total for Question 2 is 2 marks)
3
Here are the first four terms of a sequence.
1, 3, 6, 10
(a)Write down the next two terms of the sequence.(1)
(b)State the name given to this special sequence of numbers.(1)
(Total for Question 3 is 2 marks)
4
Here are the first five terms of a sequence.
2, 5, 7, 12, 19
(a)Explain how each term of the sequence, after the first two, is found from the previous two terms.(1)
(b)Work out the next term in the sequence.(1)
(Total for Question 4 is 2 marks)
5
Four sequences are shown below.
Sequence P: 5, 8, 11, 14
Sequence Q: 2, 6, 18, 54
Sequence R: 1, 1, 2, 3, 5, 8
Sequence S: 1, 4, 9, 16
(a)State whether Sequence P is arithmetic, geometric, or neither of these.(1)
  • A) Arithmetic (common difference)
  • B) Geometric (common ratio)
  • C) Neither of these
(b)State whether Sequence Q is arithmetic, geometric, or neither of these.(1)
  • A) Arithmetic (common difference)
  • B) Geometric (common ratio)
  • C) Neither of these
(c)State whether Sequence R is arithmetic, geometric, or neither of these.(1)
  • A) Arithmetic (common difference)
  • B) Geometric (common ratio)
  • C) Neither of these
(d)State whether Sequence S is arithmetic, geometric, or neither of these.(1)
  • A) Arithmetic (common difference)
  • B) Geometric (common ratio)
  • C) Neither of these
(Total for Question 5 is 4 marks)
6
The table shows the number of matchsticks used to make patterns of joined squares in a row.
Pattern number (n): 1, 2, 3
Number of matchsticks: 4, 7, 10
(a)Write down the number of matchsticks needed for Pattern number 4.(1)
(b)Find an expression, in terms of n, for the number of matchsticks in Pattern number n.(2)
(Total for Question 6 is 3 marks)
7
A sequence has nth term 5n - 2.
(a)Work out the first three terms of the sequence.(2)
(b)Work out the 20th term of the sequence.(1)
(Total for Question 7 is 3 marks)
8
Here are the first four terms of a sequence.
8, 5, 2, -1
Find an expression, in terms of n, for the nth term of the sequence.
(Total for Question 8 is 2 marks)
9
Which of these is the nth term of the sequence 7, 10, 13, 16, ...?
  • A) 3n + 4
  • B) 3n + 3
  • C) 4n + 3
  • D) 3n + 7
(Total for Question 9 is 1 mark)
10
Here are the first four terms of a sequence.
1, 1.5, 2, 2.5
(a)Write down the next term of the sequence.(1)
(b)Find an expression, in terms of n, for the nth term of the sequence.(2)
(Total for Question 10 is 3 marks)
11
The nth term of a sequence is 2n + 7. Work out which term of the sequence is equal to 35.
(Total for Question 11 is 2 marks)
12
Pattern number 1 is made from 5 tiles.
Pattern number 2 is made from 9 tiles.
Pattern number 3 is made from 13 tiles.
Each new pattern uses 4 more tiles than the pattern before it.
(a)Write down the number of tiles in Pattern number 5.(1)
(b)Find an expression, in terms of n, for the number of tiles in Pattern number n.(2)
(c)A pattern in the sequence is made from 89 tiles. Work out the pattern number.(2)
(Total for Question 12 is 5 marks)
13
A theatre has rows of seats.
Row 1 has 18 seats.
Each row after Row 1 has 4 more seats than the row before it.
(a)Find an expression, in terms of n, for the number of seats in Row n.(2)
(b)Work out the number of seats in Row 15.(2)
(c)Show that Row 19 has 90 seats.(2)
(Total for Question 13 is 6 marks)
14
The nth term of a sequence is 40 - 3n.
(a)Work out the first term and the common difference of the sequence.(2)
(b)Work out the first term in the sequence that is negative.(3)
(Total for Question 14 is 5 marks)
15
A sequence has nth term 4n + 3. Is 100 a term of this sequence? You must show working to justify your answer.
(Total for Question 15 is 2 marks)
16
A sequence has nth term 6n - 5. Show that 200 is not a term of this sequence.
(Total for Question 16 is 2 marks)
17
The nth term of a sequence is n2 + 1.
(a)Work out the first four terms of the sequence.(2)
(b)Work out the 10th term of the sequence.(1)
(Total for Question 17 is 3 marks)
18
A sequence is defined as follows.
First term = 3
Each term after the first term = 2 x (previous term) - 1
(a)Work out the first four terms of the sequence.(2)
(b)State, giving a reason, whether the sequence is arithmetic.(1)
(Total for Question 18 is 3 marks)
19
Chloe is saving money.
After Week 1, she has saved a total of 50 pounds.
After Week 2, she has saved a total of 65 pounds.
The total amount she has saved increases by the same amount each week.
(a)Find an expression, in terms of n, for the total amount, A pounds, Chloe has saved after n weeks.(2)
(b)Work out the total amount Chloe has saved after 12 weeks.(2)
(c)Chloe wants her total savings to reach at least 500 pounds. Work out the least number of complete weeks this will take.(3)
(Total for Question 19 is 7 marks)
20
Here are the first five terms of a sequence.
3, 8, 15, 24, 35
(a)Work out the first differences between consecutive terms.(1)
(b)Work out the second differences, and use this to explain why the sequence is quadratic.(2)
(c)Work out the next term in the sequence.(1)
(Total for Question 20 is 4 marks)
21
Sequence A has nth term 3n + 1.
Sequence B has nth term 5n - 4.
(a)Write down the first six terms of Sequence A and the first six terms of Sequence B.(2)
(b)Find the smallest number that appears in both Sequence A and Sequence B.(2)
(Total for Question 21 is 4 marks)
22
The nth term of a sequence is given by An + B, where A and B are numbers to be found.
The 2nd term of the sequence is 11.
The 5th term of the sequence is 23.
Work out the values of A and B.
(Total for Question 22 is 3 marks)
Mark scheme · 4.7 Sequences (Nth Term)

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22