Pack B — Fluency

Mathematics

Year 10 · Sequences

Pack B · Fluency

Name: _________________________________

Date: _________________ Class: ___________

Answer all questions. Show your working. Questions are grouped by challenge level.

BronzeQuestions 1–10

1.
Write down the next two terms in the sequence: $5,\ 9,\ 13,\ 17,\ \ldots$ .
2.
Write down the next two terms in the sequence: $3,\ 12,\ 48,\ 192,\ \ldots$ .
3.
State whether the sequence $1,\ 2,\ 4,\ 8,\ \ldots$ is arithmetic, geometric, or neither.
4.
For the sequence $20,\ 14,\ 8,\ 2,\ \ldots$ , state the common difference $d$ .
5.
For the sequence $81,\ 27,\ 9,\ 3,\ \ldots$ , state the common ratio $r$ .
6.
A sequence begins $12,\ 18,\ 24,\ 30,\ \ldots$ . Write down (a) $u_1$ and (b) $u_3$ .
7.
A sequence has first term $u_1 = 2$ and term-to-term rule "add $7$ ". Write down the first four terms.
8.
A sequence has $u_1 = 5$ and term-to-term rule "multiply by $2$ ". Write down the first four terms.
9.
The $n$ th term of a sequence is $u_n = 4n + 1$ . Find $u_1$ and $u_5$ .
10.
Find the 6th term of the sequence $7,\ 12,\ 17,\ 22,\ \ldots$ .

SilverQuestions 11–20

11.
Find the $n$ th term formula for the arithmetic sequence $3,\ 9,\ 15,\ 21,\ \ldots$ .
12.
Find the $n$ th term formula for the sequence $50,\ 45,\ 40,\ 35,\ \ldots$ .
13.
For the arithmetic sequence with $u_1 = 12$ and $d = 3$ , find $u_{{n}}$ .
14.
For the sequence with $n$ th term $u_n = 5n + 2$ , find which term equals $102$ .
15.
A geometric sequence has $u_1 = 2$ and $r = 3$ . Find $u_5$ .
16.
A sequence is defined recursively by $u_1 = 1$ and $u_{{n+1}} = u_n + 6$ . Find the first four terms.
17.
A sequence is defined by $u_1 = 4$ and $u_{{n+1}} = 3 u_n$ . Find $u_4$ .
18.
A pattern uses $5$ matchsticks for shape 1, and each new shape adds $4$ more. How many matchsticks for shape 10?
19.
An arithmetic sequence has $u_3 = 9$ and $u_8 = 24$ . Find the common difference.
20.
Find the $n$ th term formula for the geometric sequence $5,\ 10,\ 20,\ 40,\ \ldots$ .

GoldQuestions 21–30

21.
An arithmetic sequence has $u_5 = 14$ and $u_{{n}} = 44$ where $n = 15$ . Find $u_1$ and $d$ .
22.
The $n$ th term of a sequence is $u_n = 5n + 2$ . Find the first term greater than $200$ .
23.
A sequence is defined by $u_1 = 4$ and $u_{{n+1}} = 2u_n - 2$ . Find $u_4$ .
24.
A geometric sequence has $u_2 = 8$ and $u_4 = 32$ (both positive). Find $u_1$ and $r$ .
25.
A sequence is given by $1,\ 8,\ 27,\ 64,\ \ldots$ . Find the next term and describe the pattern.
26.
A sequence is defined by $u_1 = 2$ , $u_2 = 3$ and $u_{{n+1}} = u_n + u_{{n-1}}$ . Find $u_6$ .
27.
Which term of the sequence $u_n = 6n - 1$ equals $89$ ?
28.
The first three terms of a sequence are $10,\ 6,\ 2,\ -2,\ \ldots$ . (a) State the type. (b) Find $u_n$ .
29.
Find the sum of the first $12$ terms of the arithmetic sequence with $u_1 = 2$ and $d = 3$ .
30.
A geometric sequence has $u_1 = 81$ and $r = \dfrac{1}{3}$ . Find $u_4$ .

PlatinumQuestions 31–40

31.
An arithmetic sequence has $u_4 = 11$ and $u_{{n}} = 41$ where $n = 14$ . Find $u_n$ as a formula.
32.
Find the sum of all multiples of $5$ between 1 and $200$ inclusive.
33.
A geometric sequence has $u_3 = 18$ and $u_6 = 486$ (both positive). Find $u_1$ and $r$ .
34.
Sequence A has $u_n = 5n + 2$ and sequence B has $u_n = 7n - 6$ . For which value of $n$ do they have the same term?
35.
A sequence is defined by $u_1 = 12$ and $u_{{n+1}} = \dfrac{u_n}{2} + 2$ . Find $u_4$ .
36.
Find the sum of the first $5$ terms of the geometric sequence with $u_1 = 3$ and $r = 2$ .
37.
The first four terms of a sequence are $3,\ 8,\ 15,\ 24,\ \ldots$ . Find the next term and a quadratic formula for $u_n$ .
38.
A bacterial colony of $100$ cells doubles every hour. (a) Write the number of cells $u_n$ after $n$ hours. (b) After how many full hours will the population exceed $5000$ ?
39.
Maya saves £ $4$ in week 1 and £ $2$ more each week than the previous week. In which week does her **weekly** saving first exceed £ $40$ ?
40.
A sequence is defined by $u_1 = 2$ and $u_{{n+1}} = u_n + 2n + 1$ . Find $u_5$ .