Pure Mathematics - Sequences and Series Practice Questions
A-Levels · A-Level Mathematics · 145 free MCQs with instant results and detailed explanations.
145
Total
47
Easy
72
Medium
26
Hard
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Sample Questions from Pure Mathematics - Sequences and Series
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Q1
Easy
What is the 5th term of the arithmetic sequence where the first term is 3 and the common difference is 4?
A.
19
B.
15
C.
23
D.
11
Show Answer & Explanation
Correct Answer: A
In an arithmetic sequence, the nth term can be calculated using the formula: a_n = a + (n - 1)d. Here, a = 3, d = 4, and n = 5. Thus, a_5 = 3 + (5 - 1) * 4 = 3 + 16 = 19.
Q2
Easy
In a geometric sequence, if the first term is 2 and the common ratio is 3, what is the 4th term?
A.
54
B.
18
C.
36
D.
24
Show Answer & Explanation
Correct Answer: A
The nth term of a geometric sequence can be determined using the formula: a_n = a * r^(n - 1). Here, a = 2, r = 3, and n = 4. Therefore, a_4 = 2 * 3^(4 - 1) = 2 * 27 = 54.
Q3
Easy
What is the common difference of the arithmetic sequence 3, 7, 11, 15?
A.
4
B.
3
C.
5
D.
6
Show Answer & Explanation
Correct Answer: A
The common difference in an arithmetic sequence is found by subtracting any term from the subsequent term. Here, 7 - 3 = 4, 11 - 7 = 4, and 15 - 11 = 4. Thus, the common difference is 4.
Q4
Medium
If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 10th term of the sequence?
A.
32
B.
30
C.
29
D.
25
Show Answer & Explanation
Correct Answer: A
The nth term of an arithmetic sequence can be calculated using the formula a_n = a + (n-1)d. Here, a = 5, d = 3, and n = 10. Thus, a_10 = 5 + (10-1) * 3 = 5 + 27 = 32.
Q5
Medium
The sum of the first n terms of a geometric series is given by S_n = a(1 - r^n) / (1 - r). If a = 2, r = 0.5, and you want to find S_4, what is the value?
A.
3.75
B.
4
C.
2.5
D.
5
Show Answer & Explanation
Correct Answer: A
Substituting a = 2, r = 0.5, and n = 4 into the formula gives S_4 = 2(1 - (0.5)^4) / (1 - 0.5) = 2(1 - 0.0625) / 0.5 = 2(0.9375) / 0.5 = 3.75.
Q6
Medium
Given the sequence defined by a_n = n^2 - n + 1, what is the value of a_5?
A.
21
B.
19
C.
17
D.
15
Show Answer & Explanation
Correct Answer: A
Substituting n = 5 into the expression a_n = n^2 - n + 1 gives a_5 = 5^2 - 5 + 1 = 25 - 5 + 1 = 21.
Q7
Medium
If the first term of a sequence is 4 and the second term is 10, and it is known to be quadratic, what is the third term?
A.
18
B.
20
C.
22
D.
24
Show Answer & Explanation
Correct Answer: A
In a quadratic sequence, the second difference is constant. The difference between the first and second terms is 6. Assuming a common difference of 6, the third term would be 10 + 8 = 18.
Q8
Hard
The sequence defined by a_n = 2n^2 - 3n + 5 is given. What is the value of a_5?
A.
40
B.
30
C.
25
D.
15
Show Answer & Explanation
Correct Answer: A
To find a_5, substitute n = 5 into the formula: a_5 = 2(5)^2 - 3(5) + 5 = 2(25) - 15 + 5 = 50 - 15 + 5 = 40.
Q9
Hard
Consider the infinite geometric series S = 3 + 1.5 + 0.75 + ... What is the sum of this series?
A.
9
B.
6
C.
4.5
D.
12
Show Answer & Explanation
Correct Answer: B
The first term a = 3 and the common ratio r = 0.5. The sum S of an infinite geometric series is given by S = a / (1 - r). Here, S = 3 / (1 - 0.5) = 3 / 0.5 = 6.
Q10
Hard
Consider the arithmetic sequence where the first term is 5 and the common difference is 3. What is the 20th term of this sequence?
A.
62
B.
59
C.
55
D.
57
Show Answer & Explanation
Correct Answer: A
The nth term of an arithmetic sequence can be found using the formula a_n = a_1 + (n - 1)d. Here, a_1 = 5, d = 3, and n = 20. Thus, a_20 = 5 + (20 - 1) * 3 = 5 + 57 = 62.
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Pure Mathematics - Sequences and Series — A-Levels A-Level Mathematics Practice Questions Online
This page contains 145 practice MCQs for the chapter Pure Mathematics - Sequences and Series in A-Levels A-Level Mathematics. The questions are organized by difficulty — 47 easy, 72 medium, 26 hard — so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.