Sequences (Copy)
Question 1
Continue the sequence: 2, 5, 8, 11, … (next three terms).
Find the nth term of this sequence.
Question 2
A sequence is given as 10, 7, 4, 1, …
(a) Write down the next three terms.
(b) Find the nth term.
Question 3
The sequence is 1, 4, 9, 16, …
(a) Identify the type of sequence.
(b) Write the next three terms.
(c) Find the nth term.
Question 4
Consider the sequence 2, 6, 12, 20, …
(a) Find the next three terms.
(b) Show that this is a quadratic sequence.
(c) Find its nth term.
Question 5
The sequence is 3, 6, 12, 24, …
(a) Write down the next three terms.
(b) Find the term-to-term rule.
(c) State whether it is linear, quadratic, cubic or exponential.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 6
The sequence is 7, 14, 21, 28, …
(a) Continue the next three terms.
(b) Find the nth term.
Question 7
A sequence has nth term 2n − 1.
(a) Write the first five terms.
(b) Explain what kind of numbers the sequence represents.
Question 8
A sequence is given by Tn = 5n + 2.
(a) Write the first four terms.
(b) Find T15.
Question 9
The sequence is 1, 8, 27, 64, …
(a) Write the next two terms.
(b) Write the nth term.
Question 10
The sequence is 81, 27, 9, 3, …
(a) Write down the next three terms.
(b) State the type of sequence.
(c) Find the nth term in terms of powers of 3.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 11
Find the nth term of the sequence 4, 9, 14, 19, …
Question 12
A sequence has nth term Tn = n² + 3.
(a) Write the first four terms.
(b) Find T10.
Question 13
The sequence is defined as: Tn = 2ⁿ.
(a) Write the first five terms.
(b) Find T7.
Question 14
The sequence is 2, 4, 8, 16, …
(a) Find the next three terms.
(b) Write the nth term.
Question 15
A sequence is 2, 7, 14, 23, 34, …
(a) Write the next three terms.
(b) Find the nth term using the quadratic method.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 16
Find the nth term of the sequence 3, 11, 21, 33, …
Question 17
A sequence is defined as Tn = n³ + 2.
(a) Write the first four terms.
(b) Find T6.
Question 18
The sequence is 5, 10, 20, 40, …
(a) Write the next three terms.
(b) State whether the sequence is arithmetic, geometric, or neither.
(c) Find the nth term.
Question 19
The sequence is 1, 3, 7, 13, 21, …
(a) Continue the next three terms.
(b) Show that this is quadratic.
(c) Find the nth term.
Question 20
The sequence is 100, 50, 25, 12.5, …
(a) Continue the next three terms.
(b) State the ratio.
(c) Write the nth term.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 21
Find the nth term of the sequence 1, 6, 11, 16, …
Question 22
A sequence is defined by Tn = 3n² − 2n.
(a) Write the first four terms.
(b) Find T8.
Question 23
The sequence is ½, 1, 2, 4, 8, …
(a) Write the next three terms.
(b) State the type of sequence.
(c) Find the nth term.
Question 24
A sequence is given: 0, 1, 1, 2, 3, 5, 8, 13, …
(a) Write the next three terms.
(b) State what type of sequence this is.
Question 25
Find the nth term of the sequence 2, 10, 26, 50, …
Question 26
A sequence has nth term Tn = 4n − 7.
(a) Write the first four terms.
(b) Find T12.
Question 27
The sequence is −3, −1, 1, 3, 5, …
(a) Write the next three terms.
(b) Find the nth term.
Question 28
A sequence is defined by Tn = (n + 1)².
(a) Write the first four terms.
(b) Find T20.
Question 29
The sequence is 6, 12, 24, 48, …
(a) Write the next three terms.
(b) Find the nth term in terms of powers of 2.
Question 30
A sequence is defined by Tn = n² − n.
(a) Write the first five terms.
(b) Find T15.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Answer key and explanations — 7. Sequences
1.
Sequence: 2, 5, 8, 11…
Next three terms: 14, 17, 20.
nth term: Tn = 3n − 1.
Explanation: Difference = +3 each time. First term = 2 → 3(1) − 1 = 2.
2.
Sequence: 10, 7, 4, 1…
(a) Next terms: −2, −5, −8.
(b) nth term: Tn = 13 − 3n.
Explanation: Difference = −3. Check: for n=1, 13 − 3(1) = 10.
3.
Sequence: 1, 4, 9, 16…
(a) Type: Square numbers.
(b) Next terms: 25, 36, 49.
(c) nth term: Tn = n².
4.
Sequence: 2, 6, 12, 20…
(a) Next terms: 30, 42, 56.
(b) Differences: 4, 6, 8 → second difference constant = quadratic.
(c) nth term: Tn = n² + n. (Check: n=1 → 2; n=2 → 6, etc.)
5.
Sequence: 3, 6, 12, 24…
(a) Next terms: 48, 96, 192.
(b) Multiply by 2 each step.
(c) Exponential sequence. nth term: Tn = 3 × 2ⁿ⁻¹.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
6.
Sequence: 7, 14, 21, 28…
Next terms: 35, 42, 49.
nth term: Tn = 7n.
7.
nth term = 2n − 1.
(a) Terms: 1, 3, 5, 7, 9.
(b) Odd numbers.
8.
Tn = 5n + 2.
(a) First four: 7, 12, 17, 22.
(b) T15 = 5(15) + 2 = 77.
9.
Sequence: 1, 8, 27, 64…
(a) Next: 125, 216.
(b) nth term: Tn = n³.
10.
Sequence: 81, 27, 9, 3…
(a) Next: 1, 1/3, 1/9.
(b) Geometric, ratio = 1/3.
(c) nth term: Tn = 81 × (1/3)ⁿ⁻¹.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
11.
Sequence: 4, 9, 14, 19…
nth term: Tn = 5n − 1.
12.
Tn = n² + 3.
(a) 4, 7, 12, 19.
(b) T10 = 100 + 3 = 103.
13.
Tn = 2ⁿ.
(a) Terms: 2, 4, 8, 16, 32.
(b) T7 = 128.
14.
Sequence: 2, 4, 8, 16…
(a) Next: 32, 64, 128.
(b) nth term: Tn = 2ⁿ.
15.
Sequence: 2, 7, 14, 23, 34…
(a) Next: 47, 62, 79.
(b) Second differences constant → quadratic. nth term = n² + 1.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
16.
Sequence: 3, 11, 21, 33…
nth term: Tn = n² + 2n.
17.
Tn = n³ + 2.
(a) 3, 10, 29, 66.
(b) T6 = 218.
18.
Sequence: 5, 10, 20, 40…
(a) Next: 80, 160, 320.
(b) Geometric, ratio = 2.
(c) nth term: Tn = 5 × 2ⁿ⁻¹.
19.
Sequence: 1, 3, 7, 13, 21…
(a) Next: 31, 43, 57.
(b) Differences: 2, 4, 6, 8 → quadratic.
(c) nth term = n² + n − 1.
20.
Sequence: 100, 50, 25, 12.5…
(a) Next: 6.25, 3.125, 1.5625.
(b) Ratio = ½.
(c) nth term: Tn = 100 × (½)ⁿ⁻¹.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
21.
Sequence: 1, 6, 11, 16…
nth term: Tn = 5n − 4.
22.
Tn = 3n² − 2n.
(a) Terms: 1, 8, 21, 40.
(b) T8 = 3(64) − 16 = 192 − 16 = 176.
23.
Sequence: ½, 1, 2, 4, 8…
(a) Next: 16, 32, 64.
(b) Geometric ratio 2.
(c) nth term: Tn = ½ × 2ⁿ⁻¹ = 2ⁿ⁻².
24.
Sequence: 0, 1, 1, 2, 3, 5, 8, 13…
(a) Next: 21, 34, 55.
(b) Fibonacci sequence (sum of two previous terms).
25.
Sequence: 2, 10, 26, 50…
nth term: Tn = 2n³ − n.
26.
Tn = 4n − 7.
(a) Terms: −3, 1, 5, 9.
(b) T12 = 41.
27.
Sequence: −3, −1, 1, 3, 5…
(a) Next: 7, 9, 11.
(b) nth term: Tn = 2n − 5.
28.
Tn = (n + 1)².
(a) 4, 9, 16, 25.
(b) T20 = 21² = 441.
29.
Sequence: 6, 12, 24, 48…
(a) Next: 96, 192, 384.
(b) nth term: Tn = 6 × 2ⁿ⁻¹.
30.
Tn = n² − n.
(a) Terms: 0, 2, 6, 12, 20.
(b) T15 = 225 − 15 = 210.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course