A sequence has rule: start at 2 and add 6 each time. Write down the first four terms.
(2)
4
For each sequence, find an expression for the nth term in the form an + b.
(a)Sequence: 5, 8, 11, 14, ...(1)
(b)Sequence: 12, 9, 6, 3, ...(1)
(c)Sequence: 7, 11, 15, 19, ...(2)
5
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)
6
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)
7
Find n when the nth term equals 41 for the sequence with nth term 5n - 4.
(3)
8
The nth term of a sequence is 8n + 2. Is 50 a term of this sequence? If it is, find n; if it is not, explain why.
(4)
9
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)
10
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)
Mark scheme · KS3.M-A15 Linear Sequences and the nth Term
Question 1
(a) B1 next two terms 24 and 29 cao
(a) Answer: 24, 29
(b) B1 next two terms 8 and 5 cao
(b) Answer: 8, 5
(c) B1 next two terms 23 and 27 cao
(c) Answer: 23, 27
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) B1 3n + 2 cao
(a) Answer: 3n + 2
(b) B1 -3n + 15 cao
(b) Answer: -3n + 15
(c) M1 common difference 4 identified, so a = 4
(c) A1 4n + 3 cao
(c) Answer: 4n + 3
Question 5
(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 6
(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 7
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 8
M1 set up equation 8n + 2 = 50 and rearrange to 8n = 48
M1 divide both sides by 8 to find n = 6
A1 n = 6 cao
B1 explicit statement that 50 is a term since n = 6 is a positive integer (or equivalent justification)
Answer: n = 6
Question 9
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 10
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