Dãy số và Cấp số Practice Questions
THPT (Vietnam) · THPT Toán · 145 free MCQs with instant results and detailed explanations.
145
Total
49
Easy
70
Medium
26
Hard
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Sample Questions from Dãy số và Cấp số
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Q1
Easy
In a sequence of numbers, if the 4th term is 16 and the 6th term is 24, what is the common difference?
A.
4
B.
5
C.
6
D.
7
Show Answer & Explanation
Correct Answer: A
Let the first term be a and the common difference be d. The 4th term can be written as T_4 = a + 3d = 16, and the 6th term as T_6 = a + 5d = 24. Subtracting these two equations gives us 2d = 8, hence d = 4. This is the value of the common difference.
Q2
Easy
What is the sum of the first 10 terms of the arithmetic sequence where the first term is 2 and the common difference is 3?
A.
155
B.
100
C.
120
D.
140
Show Answer & Explanation
Correct Answer: A
The formula for the sum of the first n terms of an arithmetic sequence is S_n = n/2 * (2a + (n-1)d). Here, n = 10, a = 2, and d = 3. Therefore, S_10 = 10/2 * (2*2 + (10-1)*3) = 5 * (4 + 27) = 5 * 31 = 155.
Q3
Easy
If the first term of a geometric sequence is 4 and the common ratio is 2, what is the 5th term?
A.
16
B.
32
C.
64
D.
128
Show Answer & Explanation
Correct Answer: C
In a geometric sequence, the nth term is calculated as a_n = ar^(n-1). Here, a = 4, r = 2, and n = 5. Therefore, a_5 = 4 * 2^(5-1) = 4 * 16 = 64.
Q4
Medium
In an arithmetic sequence, the first term is 5 and the common difference is 3. What is the 10th term of the sequence?
A.
32
B.
30
C.
29
D.
35
Show Answer & Explanation
Correct Answer: A
The n-th term of an arithmetic sequence can be calculated using the formula a_n = a_1 + (n - 1)d. Here, a_1 = 5, d = 3, and n = 10. Therefore, a_10 = 5 + (10 - 1) * 3 = 5 + 27 = 32.
Q5
Medium
A geometric series has a first term of 4 and a common ratio of 2. What is the sum of the first 5 terms of this series?
A.
124
B.
60
C.
63
D.
80
Show Answer & Explanation
Correct Answer: A
The sum of the first n terms of a geometric series can be calculated using the formula S_n = a_1 * (1 - r^n) / (1 - r), where a_1 = 4, r = 2, and n = 5. Therefore, S_5 = 4 * (1 - 2^5) / (1 - 2) = 4 * (1 - 32) / (-1) = 4 * 31 = 124.
Q6
Medium
If the arithmetic sequence is defined by the formula a_n = 2n + 1, what is the 15th term of the sequence?
A.
31
B.
29
C.
30
D.
28
Show Answer & Explanation
Correct Answer: A
To find the 15th term of the sequence defined by a_n = 2n + 1, substitute n = 15 into the equation. Thus, a_15 = 2(15) + 1 = 30 + 1 = 31.
Q7
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.
29
D.
25
Show Answer & Explanation
Correct Answer: A
In an arithmetic sequence, the nth term can be calculated using 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 = 5 + 27 = 32.
Q8
Hard
If the sum of the first n terms of an arithmetic series is given by S_n = 2n^2 + 3n, what is the common difference of the series?
A.
4
B.
6
C.
5
D.
2
Show Answer & Explanation
Correct Answer: C
To find the common difference, we first find the first term (a_1) and the second term (a_2) using the sum formula. The common difference can be found as d = a_2 - a_1. Here, S_1 = 5 and S_2 = 10. Therefore, d = S_2 - S_1 = 10 - 5 = 5.
Q9
Hard
Given the arithmetic sequence where the first term is 5 and the common difference is 3, what is the 10th term of the sequence?
A.
32
B.
35
C.
30
D.
29
Show Answer & Explanation
Correct Answer: A
The 10th term of an arithmetic sequence can be found using the formula: a_n = a + (n - 1)d. Here, a = 5, n = 10, and d = 3, so a_10 = 5 + (10 - 1) * 3 = 5 + 27 = 32.
Q10
Hard
In a geometric sequence, the first term is 4 and the ratio between consecutive terms is 2. What is the 6th term of this sequence?
A.
128
B.
64
C.
32
D.
16
Show Answer & Explanation
Correct Answer: A
The nth term of a geometric sequence is given by the formula: a_n = a * r^(n - 1). Here, a = 4, r = 2, and n = 6, so a_6 = 4 * 2^(6 - 1) = 4 * 32 = 128.
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Dãy số và Cấp số — THPT (Vietnam) THPT Toán Practice Questions Online
This page contains 145 practice MCQs for the chapter Dãy số và Cấp số in THPT (Vietnam) THPT Toán. The questions are organized by difficulty — 49 easy, 70 medium, 26 hard — so you can choose the right level for your preparation.
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