Patterns Sequences and Series Practice Questions
Matric (South Africa) · Matric Mathematics · 141 free MCQs with instant results and detailed explanations.
141
Total
49
Easy
74
Medium
18
Hard
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Sample Questions from Patterns Sequences and Series
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Q1
Easy
If the next term in the sequence 2, 4, 8, 16 is to be found, what is it?
A.
32
B.
64
C.
24
D.
20
Show Answer & Explanation
Correct Answer: A
The sequence is a geometric progression where each term is multiplied by 2. The next term after 16 is 16 * 2 = 32.
Q2
Easy
In the series 1, 1/2, 1/4, 1/8, which type of series is this and what will be the 5th term?
A.
Geometric, 1/16
B.
Arithmetic, 1/16
C.
Geometric, 1/8
D.
Fibonacci, 1/16
Show Answer & Explanation
Correct Answer: A
This series is geometric because each term is half of the previous term (common ratio of 1/2). The 5th term is 1/8 * (1/2) = 1/16.
Q3
Easy
What is the 5th term in the arithmetic sequence where the first term is 2 and the common difference is 3?
A.
14
B.
15
C.
17
D.
18
Show Answer & Explanation
Correct Answer: A
The 5th term can be calculated using the formula for the nth term of an arithmetic sequence: a_n = a + (n-1)d. Here, a = 2, d = 3, and n = 5. Thus, a_5 = 2 + (5-1) * 3 = 2 + 12 = 14.
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.
30
C.
27
D.
25
Show Answer & Explanation
Correct Answer: A
The nth term of an arithmetic sequence is given by the formula: a_n = a_1 + (n-1)d. Here, a_1 = 5, d = 3, and n = 10. Thus, a_10 = 5 + (10-1) * 3 = 32.
Q5
Medium
If the sum of the first n terms of a geometric series is given by S_n = 8(1 - (1/2)^n)/ (1 - 1/2), what is the 4th term of the series?
A.
2
B.
4
C.
8
D.
1
Show Answer & Explanation
Correct Answer: B
The series is geometric with a first term of 8 and a common ratio of 1/2. The nth term can be found using T_n = a * r^(n-1). For the 4th term, T_4 = 8 * (1/2)^(4-1) = 8 * (1/8) = 4.
Q6
Medium
Which of the following sequences is neither arithmetic nor geometric?
A.
2, 5, 8, 11
B.
3, 9, 27, 81
C.
1, 4, 9, 16
D.
2, 4, 8, 16
Show Answer & Explanation
Correct Answer: C
The sequence 1, 4, 9, 16 consists of square numbers (n^2). It does not have a constant difference (arithmetic) or a constant ratio (geometric), thus it is neither.
Q7
Medium
A sequence is defined by the recursive formula a_n = 3a_(n-1) + 2 with a_1 = 1. What is the value of a_4?
A.
26
B.
28
C.
30
D.
32
Show Answer & Explanation
Correct Answer: A
To find a_4, we calculate each term using the recursive formula: a_2 = 3 * 1 + 2 = 5; a_3 = 3 * 5 + 2 = 17; a_4 = 3 * 17 + 2 = 53. Thus, a_4 = 26.
Q8
Hard
A geometric sequence has a first term of 3 and a common ratio of 2. What is the 5th term of this sequence?
A.
48
B.
24
C.
12
D.
6
Show Answer & Explanation
Correct Answer: A
In a geometric sequence, each term is obtained by multiplying the previous term by the common ratio. The formula for the nth term is given by a_n = a * r^(n-1). Here, a = 3, r = 2, and n = 5. Hence, a_5 = 3 * 2^(5-1) = 3 * 16 = 48.
Q9
Hard
In an arithmetic sequence, the first term is 12 and the common difference is 5. What is the 15th term of this sequence?
A.
72
B.
82
C.
77
D.
67
Show Answer & Explanation
Correct Answer: B
To find the nth term of an arithmetic sequence, use the formula: a_n = a + (n-1)d, where a is the first term and d is the common difference. Here, a = 12, d = 5, and n = 15. Thus, a_15 = 12 + (15-1) * 5 = 12 + 70 = 82.
Q10
Hard
A geometric sequence has a first term of 3 and a common ratio of 2. What is the sum of the first 6 terms?
A.
189
B.
186
C.
191
D.
195
Show Answer & Explanation
Correct Answer: A
The sum of the first n terms of a geometric sequence can be calculated using the formula S_n = a(1 - r^n) / (1 - r), where a is the first term and r is the common ratio. Here, S_6 = 3(1 - 2^6) / (1 - 2) = 3(1 - 64) / (-1) = 3 * 63 = 189.
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Patterns Sequences and Series — Matric (South Africa) Matric Mathematics Practice Questions Online
This page contains 141 practice MCQs for the chapter Patterns Sequences and Series in Matric (South Africa) Matric Mathematics. The questions are organized by difficulty — 49 easy, 74 medium, 18 hard — so you can choose the right level for your preparation.
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