Linear Sequences and the nth Term - Worksheets, Questions and Revision

23 original exam-style questions - 6 pages of questions with a full mark scheme - free printable PDF.

Download PDF Jump to mark scheme (page 7)Linear Sequences and the nth Term revision guide

This topic is chapter 2 of KS3 Maths: Algebra Practice Book 2.

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2.15 Linear Sequences and the nth Term

AQA KS3.M-A15 · Calculators not allowed · about 70 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Stretch: The nth term of a sequence is given by an + b. The first term is 11 and the 5th term is 31. Find the values of a and b, then state the 8th term.

(4)

State the term-to-term rule for each sequence.

(a)Sequence: 3, 6, 9, 12, ...(1)

(b)Sequence: 50, 45, 40, 35, ...(1)

A sequence has rule: start at 2 and add 6 each time. Write down the first four terms.

(2)

Given the nth term 6n - 4, work out the 5th term and the 0th term.

(a)Find the 5th term.(2)

(b)Find the 0th term.(2)

A sequence begins 2, 5, 8, 11, ... and the nth term is 3n - 1.

(a)Show that the 4th term from the nth term formula is 11.(1)

(b)Write down the 10th term.(2)

Find n when the nth term equals 41 for the sequence with nth term 5n - 4.

(3)

A gardener plants bulbs in a straight line. On the first day she plants 7 bulbs and each day after she plants 4 more than the previous day. Let the nth day have nth term 4n + 3. On which day will she first have planted at least 35 bulbs in that single day?

(3)

For each sequence give the next two terms.

(a)Sequence: 8, 11, 14, 17, ...(1)

(b)Sequence: 30, 26, 22, 18, ...(1)

(c)Sequence: 9, 13, 17, 21, ...(1)

Find the nth term of the sequence 2, 9, 16, 23, ...

(2)

Given the nth term 3n + 8, find the 6th term.

(1)

Find the 15th term of the sequence with nth term 7n - 3.

(2)

State whether the sequence 5, 8, 11, 14, ... is increasing or decreasing, and give its common difference.

(1)

A gardener plants tulip bulbs in rows. The first row has 9 bulbs and each row after has 5 more bulbs than the previous row, so the nth row has nth term 5n + 4 bulbs. On which row will she first plant at least 54 bulbs in that single row?

(3)

The nth term of a sequence is given by an + b. The first term is 9 and the 6th term is 34. Find the values of a and b, then state the 10th term.

(3)

A sequence is formed using the rule 'multiply the term number by 8, then subtract 6' to give the nth term. A student says the 100th term is 800. Is the student correct? Justify your answer with a calculation.

(3)

Priya saves money each week. She saves £12 in week 1, and each week after she saves £3 more than the previous week.

(a)Find a formula for her savings, Sn pounds, in week n.(1)

(b)Find her savings in week 9.(1)

(c)In which week does she first save more than £50 in that single week?(2)

State the term-to-term rule for each sequence.

(a)Sequence: 4, 8, 12, 16, ...(1)

(b)Sequence: 60, 52, 44, 36, ...(1)

A sequence has rule: start at 5 and add 7 each time. Write down the first four terms.

(1)

For each sequence, find an expression for the nth term in the form an + b.

(a)Sequence: 6, 10, 14, 18, ...(1)

(b)Sequence: 15, 11, 7, 3, ...(1)

(c)Sequence: 9, 13, 17, 21, ...(1)

Given the nth term 7n - 3, work out the 5th term and the 0th term.

(2)

Find n when the nth term equals 45 for the sequence with nth term 6n - 3.

(1)

The nth term of a sequence is 9n + 4. Is 60 a term of this sequence? If it is, find n; if it is not, explain why.

(2)

State the common difference of the sequence 50, 43, 36, 29, ...

(1)

Mark scheme · 2.15 Linear Sequences and the nth Term

Question 1

M1 use first term: a(1) + b = 11 or a + b = 11
M1 use fifth term: a(5) + b = 31 or 5a + b = 31 and subtract to find 4a = 20
A1 a = 5 cao
A1 b = 6 and 8th term = 5(8) + 6 = 46 cao
Answer: a = 5, b = 6; 8th term = 46

Question 2

(a) B1 add 3 each time cao
(a) Answer: Add 3 each time
(b) B1 subtract 5 each time cao
(b) Answer: Subtract 5 each time

Question 3

M1 list showing repeated addition by 6
A1 2, 8, 14, 20 cao
Answer: 2, 8, 14, 20

Question 4

(a) M1 substitute n = 5 into 6n - 4
(a) A1 26 cao
(a) Answer: 26
(b) M1 substitute n = 0 into 6n - 4
(b) A1 -4 cao
(b) Answer: -4

Question 5

(a) B1 substitution n = 4 gives 11 cao
(a) Answer: 11
(b) M1 substitute n = 10 into 3n - 1
(b) A1 29 cao
(b) Answer: 29

Question 6

M1 set up equation 5n - 4 = 41 or 5n = 45
M1 divide both sides by 5 or perform correct arithmetic to get n = 9
A1 n = 9 cao
Answer: n = 9

Question 7

M1 set up inequality 4n + 3 ≥ 35 and rearrange to 4n ≥ 32
M1 divide by 4 to get n ≥ 8
A1 first day is n = 8 cao
Answer: 8

Question 8

(a) B1 20, 23 cao
(a) Answer: 20, 23
(b) B1 14, 10 cao
(b) Answer: 14, 10
(c) B1 25, 29 cao
(c) Answer: 25, 29

Question 9

M1 identifies common difference 7
A1 7n - 5 cao
Answer: 7n - 5

Question 10

B1 26 cao
Answer: 26

Question 11

M1 substitutes n = 15
A1 102 cao
Answer: 102

Question 12

B1 increasing, common difference 3
Answer: Increasing, common difference 3

Question 13

M1 sets up 5n + 4 ≥ 54
M1 correct rearrangement, e.g. n ≥ 10
A1 row 10 cao
Answer: Row 10

Question 14

M1 forms and solves a + b = 9 and 6a + b = 34 simultaneously, e.g. 5a = 25
A1 a = 5, b = 4
B1 10th term = 54 (ft their a and b)
Answer: a = 5, b = 4, 10th term = 54

Question 15

M1 writes the nth term as 8n - 6 and substitutes n = 100
A1 correctly finds the 100th term is 794
B1 states the student is incorrect, since 794 does not equal 800
Answer: No, the 100th term is 794, not 800

Question 16

(a) B1 Sn = 3n + 9 cao
(a) Answer: Sn = 3n + 9
(b) B1 36 cao (ft their formula)
(b) Answer: £36
(c) M1 sets up 3n + 9 > 50
(c) A1 week 14 cao
(c) Answer: Week 14

Question 17

(a) B1 start at 4, add 4 oe
(a) Answer: start at 4, add 4 each time
(b) B1 start at 60, subtract 8 oe
(b) Answer: start at 60, subtract 8 each time

Question 18

B1 5, 12, 19, 26 cao
Answer: 5, 12, 19, 26

Question 19

(a) B1 4n + 2 cao
(a) Answer: 4n + 2
(b) B1 19 - 4n oe (-4n + 19)
(b) Answer: 19 - 4n
(c) B1 4n + 5 cao
(c) Answer: 4n + 5

Question 20

B1 5th term = 32 cao
B1 0th term = -3 cao
Answer: 5th term = 32, 0th term = -3

Question 21

B1 n = 8 cao
Answer: n = 8

Question 22

M1 sets up 9n + 4 = 60 and attempts to solve for n
A1 correct conclusion: no, since n = 56/9 is not a whole number
Answer: No, n = 56/9 is not a whole number

Question 23

B1 -7 cao
Answer: -7

Linear Sequences and the nth Term - Worksheets, Questions and Revision

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