Sequences (Copy)
IGCSE Mathematics 0580 – CORE Practice Exam
Topic: Sequences (Linear, Quadratic, Term Rules, nth Term)
With Full Worked Solutions
Paper 1 – Non-Calculator Section
Q1.
Write the next two terms in the sequence:
3, 6, 9, 12, …
Solution:
This is a linear sequence (+3 each time)
Next terms: 12 + 3 = 15, then 15 + 3 = 18
Answer: 15, 18
Q2.
Write the next two terms in the sequence:
1, 3, 6, 10, 15, …
Solution:
Term-to-term differences: +2, +3, +4, +5
Next difference = +6 → 15 + 6 = 21
Then +7 → 21 + 7 = 28
Answer: 21, 28
Q3.
Find the nth term of the sequence:
5, 8, 11, 14, …
Solution:
Difference = +3 → nth term = 3n + ?
Use 1st term:
3(1) + b = 5 → b = 2
Answer: nth term = 3n + 2
Q4.
Find the nth term of the sequence:
10, 7, 4, 1, …
Solution:
Difference = –3 → nth term = –3n + ?
Use 1st term:
–3(1) + b = 10 → b = 13
Answer: nth term = –3n + 13
Q5.
The nth term of a sequence is given by:
T(n) = 4n – 1
Find the 6th term.
Solution:
T(6) = 4(6) – 1 = 24 – 1 = 23
Answer: 23
Paper 2 – Calculator Allowed Section
Q6.
Find the nth term of the sequence:
2, 5, 10, 17, 26
Solution:
1st differences: +3, +5, +7, +9
2nd differences: +2 → Quadratic
Try n² + ? →
n² = 1, 4, 9, 16, 25
Compare with sequence: +1 each time
Answer: nth term = n² + 1
Q7.
Find the 8th term of the sequence:
T(n) = n² + 2n
Solution:
T(8) = 8² + 2×8 = 64 + 16 = 80
Answer: 80
Q8.
The 5th term of a sequence is 45.
The nth term is given by: T(n) = 2n² + 1
Verify this.
Solution:
T(5) = 2(5)² + 1 = 2×25 + 1 = 50 + 1 = 51
≠45 → So the formula does not match
Answer: The formula is incorrect for the 5th term.
Q9.
Which of the following sequences is a linear sequence?
A) 1, 3, 5, 7
B) 1, 4, 9, 16
C) 2, 5, 10, 17
D) 1, 8, 27, 64
Solution:
A) +2 each time → linear
Others are square, quadratic, and cubic respectively
Answer: A
Q10.
The nth term of a sequence is T(n) = 2n + 3.
What is the first term greater than 20?
Solution:
2n + 3 > 20 → 2n > 17 → n > 8.5
Smallest integer: n = 9
T(9) = 2(9) + 3 = 21
Answer: 21
This practice exam covers all CORE-level skills: continuing sequences, identifying term rules, finding nth terms (linear & quadratic), and applying them to solve problems.