Sequences and Series Practice Questions
KCSE (Kenya) · KCSE Mathematics · 142 free MCQs with instant results and detailed explanations.
142
Total
50
Easy
71
Medium
21
Hard
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Sample Questions from Sequences and Series
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Q1
Easy
What is the 7th term of the arithmetic sequence where the first term is 3 and the common difference is 2?
A.
15
B.
13
C.
17
D.
11
Show Answer & Explanation
Correct Answer: A
In an arithmetic sequence, the nth term can be found using the formula: a_n = a_1 + (n-1)d. Here, a_1 = 3, d = 2, and n = 7. Therefore, a_7 = 3 + (7-1) * 2 = 3 + 12 = 15.
Q2
Easy
If the sum of the first five terms of an arithmetic series is 50, what is the first term if the common difference is 5?
A.
5
B.
10
C.
15
D.
20
Show Answer & Explanation
Correct Answer: B
The sum of the first n terms of an arithmetic series is S_n = n/2 * (2a + (n-1)d). For n = 5, S_5 = 50, and d = 5. Substituting gives 50 = 5/2 * (2a + 20). Solving this leads to a = 10.
Q3
Easy
What is the common difference in the arithmetic sequence 5, 8, 11, 14?
A.
3
B.
4
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, 8 - 5 = 3, so the common difference is 3.
Q4
Medium
What is the 10th term of the arithmetic sequence where the first term is 5 and the common difference is 3?
A.
32
B.
27
C.
30
D.
35
Show Answer & Explanation
Correct Answer: A
In an arithmetic sequence, the nth term is given by 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
If the sum of the first n terms of an arithmetic series is given by S_n = 4n^2 + 2n, what is the common difference?
A.
8
B.
4
C.
2
D.
6
Show Answer & Explanation
Correct Answer: B
To find the common difference, we need to find S_n and S_{n-1}. The common difference is S_n - S_{n-1} = 4n^2 + 2n - (4(n-1)^2 + 2(n-1)). Upon simplification, it results in 4, which is the common difference.
Q6
Medium
A geometric sequence has the first term of 2 and the common ratio of 3. What is the 5th term of this sequence?
A.
162
B.
81
C.
54
D.
27
Show Answer & Explanation
Correct Answer: A
In a geometric sequence, the nth term is given by the formula a_n = a * r^(n-1). Here, a = 2, r = 3, and n = 5. So, a_5 = 2 * 3^(5-1) = 2 * 81 = 162.
Q7
Medium
In an arithmetic sequence, the 4th term is 20 and the 8th term is 36. What is the first term?
A.
4
B.
6
C.
8
D.
10
Show Answer & Explanation
Correct Answer: B
Let the first term be a and the common difference be d. The equations are: a + 3d = 20 and a + 7d = 36. Solving these gives d = 4 and a = 6.
Q8
Hard
A sequence is defined by the formula a_n = 3n + 2. What is the value of a_8?
A.
26
B.
24
C.
30
D.
20
Show Answer & Explanation
Correct Answer: A
To find a_8, substitute n with 8 in the formula. a_8 = 3(8) + 2 = 24 + 2 = 26, which makes option A the correct answer.
Q9
Hard
The first term of an arithmetic series is 5 and the common difference is 3. What is the sum of the first 15 terms of this series?
A.
240
B.
180
C.
210
D.
300
Show Answer & Explanation
Correct Answer: B
The formula for the sum of the first n terms of an arithmetic series is S_n = n/2 * (2a + (n - 1)d). Here, n = 15, a = 5, and d = 3. Plugging in these values gives S_15 = 15/2 * (2(5) + (15 - 1)3) = 15/2 * (10 + 42) = 15/2 * 52 = 180, making option B the correct answer.
Q10
Hard
The sum of the first n terms of a geometric series is given by S_n = a(1 - r^n) / (1 - r). If the first term a is 2, the common ratio r is 3, and the sum of the first 5 terms is to be calculated, what is S_5?
A.
242
B.
242/2
C.
242/3
D.
243
Show Answer & Explanation
Correct Answer: A
Using the formula for the sum of a geometric series, S_n = a(1 - r^n) / (1 - r), with a = 2, r = 3, and n = 5, we find S_5 = 2(1 - 3^5) / (1 - 3). Calculating gives S_5 = 2(1 - 243) / (-2) = 2*(-242)/(-2) = 242.
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Sequences and Series — KCSE (Kenya) KCSE Mathematics Practice Questions Online
This page contains 142 practice MCQs for the chapter Sequences and Series in KCSE (Kenya) KCSE Mathematics. The questions are organized by difficulty — 50 easy, 71 medium, 21 hard — so you can choose the right level for your preparation.
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