A sequence has rule: start at 5 and add 7 each time. Write down the first four terms.
(1)
4
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)
5
Given the nth term 7n - 3, work out the 5th term and the 0th term.
(2)
6
A sequence begins 3, 7, 11, ... and the nth term is 4n - 1.
(a)Show that the 4th term from the nth term formula is 15.(1)
(b)Write down the 10th term.(1)
7
Find n when the nth term equals 45 for the sequence with nth term 6n - 3.
(1)
8
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)
9
State the common difference of the sequence 50, 43, 36, 29, ...
(1)
10
Find the nth term of the sequence 2, 9, 16, 23, ...
(2)
11
Given the nth term 3n + 8, find the 6th term.
(1)
12
Find the 15th term of the sequence with nth term 7n - 3.
(2)
13
State whether the sequence 5, 8, 11, 14, ... is increasing or decreasing, and give its common difference.
(1)
14
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)
15
A row of n squares built from matchsticks needs a number of matchsticks given by the nth term 3n + 1.
(a)How many matchsticks are needed for 12 squares?(2)
(b)How many squares can be made with exactly 40 matchsticks?(2)
16
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)
17
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)
18
Priya saves money each week. She saves 12 pounds in week 1, and each week after she saves 3 pounds 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 pounds in that single week?(2)
Mark scheme · KS3.M-A15D Linear Sequences and the nth Term: Fluency and Exam Drill
Question 1
(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 2
(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 3
B1 5, 12, 19, 26 cao
Answer: 5, 12, 19, 26
Question 4
(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 5
B1 5th term = 32 cao
B1 0th term = -3 cao
Answer: 5th term = 32, 0th term = -3
Question 6
(a) B1 4(4) - 1 = 15 shown
(a) Answer: 15
(b) B1 39 cao
(b) Answer: 39
Question 7
B1 n = 8 cao
Answer: n = 8
Question 8
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 9
B1 -7 cao
Answer: -7
Question 10
M1 identifies common difference 7
A1 7n - 5 cao
Answer: 7n - 5
Question 11
B1 26 cao
Answer: 26
Question 12
M1 substitutes n = 15
A1 102 cao
Answer: 102
Question 13
B1 increasing, common difference 3
Answer: Increasing, common difference 3
Question 14
M1 sets up 5n + 4 ≥ 54
M1 correct rearrangement, e.g. n ≥ 10
A1 row 10 cao
Answer: Row 10
Question 15
(a) M1 substitutes n = 12
(a) A1 37 cao
(a) Answer: 37
(b) M1 sets up 3n + 1 = 40
(b) A1 n = 13 cao
(b) Answer: 13
Question 16
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 17
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