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Mathematics for IGCSE & O level - Sequences (Section 2)

1
What is the term-to-term rule for the sequence: 2, 5, 10, 17, 26, ...?
Answer
(B)
add consecutive odd numbers starting from 3
2
What is the next term in the sequence: 36, 31, 26, 21, ...?
Answer
(B)
16
3
The nth term of a sequence is given by \(U_n = n^2 + 2n\). What is the value of \(U_3\)?
Answer
(A)
12
4
What is the next term in the sequence: 11, 7, 3, -1, ...?
Answer
(B)
-5
5
Identify the sequences that are quadratic sequences.
Answer
A
C
6
Which of the following sequences is a quadratic sequence?
Answer
(C)
1, 4, 7, 10, ...
7
If the general formula for a sequence is \(T_n = 4n - 1\), then what is the 4th term?
Answer
(C)
15
8
What are the first three terms of a sequence defined by the formula \(a_n = n^2 + 1\)?
Answer
(B)
2, 5, 10
9
What is the difference between the 5th and 3rd terms in the sequence defined by \(a_n = 2n^2 - 1\)?
Answer
(C)
32
10
What is the next number in the sequence: 1, 8, 27, 64, ...?
Answer
(B)
125
11
If a sequence follows the rule \(a_n = a_{n-1} + 4\), and \(a_1 = 2\), then what is \(a_3\)?
Answer
(C)
10
12
Which of the following is the next term of the quadratic sequence 8, 13, 20, 29, 40, ...?
Answer
(A)
53
13
What is the 5th term of the sequence 2, 6, 10, 14,...?
Answer
(A)
16
14
What is the constant difference in the sequence: 14, 11, 8, 5, ...?
Answer
(B)
-3
15
Find the first four terms of the sequence defined by the formula \(U_n = 3n - 1\).
Answer
(A)
2, 5, 8, 11
16
What is the formula for the nth term of the sequence 7, 10, 13, 16,...?
Answer
(D)
4n + 3
17
If the nth term of a sequence is \(n^2 - 4\), what is the third term?
Answer
(A)
5
18
Which rule defines the sequence 8, 15, 22, 29, 36, ...?
Answer
(A)
7n + 1
19
Find the 10th term of the sequence with the nth term given by \(U_n = 5n - 2\).
Answer
(A)
43
20
The nth term of a sequence is given by \(T_n = 2n^2 + 5\). What is T2?
Answer
(A)
9
21
Which of the following sequences is a linear sequence?
Answer
(B)
75, 72, 68,...
22
Which of the following sequences is geometric?
Answer
(B)
1, 2, 4, 8, ...
23
What type of sequence has a constant second difference?
Answer
(C)
Quadratic Sequence
24
Determine the next three terms of the sequence: 2, 9, 16, 23, ...
Answer
(B)
29, 36, 43
25
In the sequence 5, 12, 19, 26, ..., what is the common difference?
Answer
(C)
7
26
Find the general formula for the nth term of the sequence 2, 7, 12, 17, ...
Answer
(A)
5n - 3
27
What is the common difference in the following arithmetic sequence: -3, 2, 7, 12, ...?
Answer
(B)
5
28
Find the nth term formula for the sequence 4, 7, 12, 19, 28,...
Answer
(C)
n^2 + 3n
29
What is the 5th term of the sequence defined by \(a_n = 2n + 1\) ?
Answer
(B)
10
30
What is the second difference in the sequence 2, 5, 10, 17, 26...?
Answer
(B)
2
31
Which of these sequences is *not* a linear sequence?
Answer
(C)
1, 4, 9, 16, ...
32
Which of these is a quadratic sequence?
Answer
(B)
1, 4, 9, 16, ...
33
What kind of sequence is represented by the formula an + b?
Answer
(D)
Linear
34
If the pattern is to subtract 7 from the previous term, and the first term is 50, what is the 4th term?
Answer
(C)
36
35
Which of these sequences is geometric?
Answer
(B)
2, 4, 8, 16, ...
36
If the first five terms of a sequence are \(\frac{2}{3}, \frac{4}{6}, \frac{6}{9}, \frac{8}{12}, \frac{10}{15}\), what is the nth term?
Answer
(B)
\(\frac{2n}{3}\)
37
Given the sequence 11, 7, 3, -1, ..., what is the nth term?
Answer
(A)
-4n + 15
38
The nth term of a sequence is given by 2n + 7. What is the 5th term?
Answer
(B)
19
39
What type of sequence is described by the general formula an^2 + bn + c?
Answer
(D)
Quadratic
40
If the nth term of a sequence is 4n - 3, what is the 6th term?
Answer
(A)
19
41
Which of the following is the term-to-term rule for the sequence 100, 90, 80, 70,...?
Answer
(B)
Subtract 10
42
Which of the following is a linear sequence?
Answer
(C)
3, 5, 7, 9, ...
43
Consider the sequence given by the formula \(T_n = 2n^2 - 1\). What are the first three terms?
Answer
A
B
C
44
The formula for the nth term of a sequence is \(T_n = n^2 - 1\). What is the second term?
Answer
(D)
3
45
If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the third term?
Answer
(B)
11
46
The formula for the nth term of a sequence is n2 - 1. What is the third term of the sequence?
Answer
(D)
8
47
What is the next term in the sequence: 7, 11, 15, 19,...?
Answer
(C)
24
48
What is the next number in the sequence 0, 1, 1, 2, 3, 5, 8, ...?
Answer
(C)
13
49
What is the next term in the sequence: 10, 14, 18, 22, ...?
Answer
(C)
28
50
What is the next term in the sequence: -2, 1, 6, 13,...?
Answer
(C)
24