Q. A certain arithmetic progression has a first term of 10 and a last term of 100. If there are 20 terms in total, what is the common difference?
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Solution
The last term of an AP is given by a + (n-1)d. Here, 100 = 10 + (20-1)d. Solving gives d = 5.
Correct Answer: A — 5
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Q. A sequence is defined as follows: 2, 5, 8, 11, ... What is the 15th term of this sequence?
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Solution
The first term a = 2 and the common difference d = 3. The 15th term = a + (15-1)d = 2 + 42 = 44.
Correct Answer: B — 41
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Q. If the 2nd term of an arithmetic progression is 8 and the 5th term is 14, what is the 3rd term?
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Solution
Let the first term be a and the common difference be d. From the equations a + d = 8 and a + 4d = 14, we can find the 3rd term a + 2d = 10.
Correct Answer: A — 10
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Q. If the 5th term of an arithmetic progression is 15 and the 10th term is 30, what is the common difference?
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Solution
Let the first term be a and the common difference be d. From the equations a + 4d = 15 and a + 9d = 30, we can find d = 3.
Correct Answer: A — 3
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Q. If the 6th term of an arithmetic progression is 30 and the 9th term is 45, what is the common difference?
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Solution
Let the first term be a and the common difference be d. From the equations a + 5d = 30 and a + 8d = 45, we can find d = 5.
Correct Answer: A — 5
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Q. If the 7th term of an arithmetic progression is 50 and the common difference is 5, what is the first term?
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Solution
Using the formula for the nth term, a + 6d = 50. Substituting d = 5 gives a + 30 = 50, hence a = 20.
Correct Answer: B — 30
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Q. If the first term of an arithmetic progression is 12 and the last term is 48, with a total of 10 terms, what is the common difference?
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Solution
The last term can be expressed as a + (n-1)d. Here, 48 = 12 + 9d. Solving gives d = 4.
Correct Answer: A — 4
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Q. If the first term of an arithmetic progression is 7 and the common difference is -2, what is the 8th term?
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Solution
Using the formula for the nth term, a + (n-1)d = 7 + (8-1)(-2) = 7 - 14 = -7.
Correct Answer: A — -1
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Q. If the sum of the first n terms of an arithmetic progression is given by S_n = 3n^2 + 2n, what is the common difference?
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Solution
The sum of the first n terms S_n = n/2 * (2a + (n-1)d). By differentiating S_n with respect to n, we can find the common difference. The common difference is 3.
Correct Answer: A — 3
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Q. In an arithmetic progression, if the 3rd term is 15 and the 6th term is 24, what is the common difference?
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Solution
Let the first term be a and the common difference be d. From the equations a + 2d = 15 and a + 5d = 24, we can solve for d, which gives d = 3.
Correct Answer: B — 4
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Q. In an arithmetic progression, if the 4th term is 20 and the 7th term is 26, what is the first term?
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Solution
Let the first term be a and the common difference be d. From the equations a + 3d = 20 and a + 6d = 26, we can solve for a and find it to be 12.
Correct Answer: B — 12
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Q. In an arithmetic progression, if the 5th term is 20 and the 10th term is 35, what is the first term?
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Solution
Let the first term be a and the common difference be d. From the given terms, we have a + 4d = 20 and a + 9d = 35. Solving these gives a = 10.
Correct Answer: B — 10
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Q. In an arithmetic progression, if the first term is 12 and the last term is 48, and there are 10 terms, what is the common difference?
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Solution
Using the formula for the last term, 48 = 12 + (10-1)d. Solving gives d = 4.
Correct Answer: A — 4
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Q. In an arithmetic progression, if the first term is 5 and the common difference is 3, what is the 10th term?
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Solution
The nth term of an AP is given by a + (n-1)d. Here, a = 5, d = 3, and n = 10. So, the 10th term = 5 + (10-1) * 3 = 5 + 27 = 32.
Correct Answer: A — 32
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Q. In an arithmetic progression, if the sum of the first 10 terms is 250, what is the first term if the common difference is 5?
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Solution
Using the formula S_n = n/2 * (2a + (n-1)d), we can substitute n = 10 and d = 5 to find a = 20.
Correct Answer: B — 20
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Q. What is the sum of the first 15 terms of an arithmetic progression where the first term is 2 and the common difference is 4?
A.
120
B.
130
C.
140
D.
150
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Solution
The sum of the first n terms S_n = n/2 * (2a + (n-1)d). Here, S_15 = 15/2 * (2*2 + 14*4) = 15/2 * (4 + 56) = 15/2 * 60 = 450.
Correct Answer: A — 120
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Q. Which of the following sequences is an arithmetic progression?
A.
2, 4, 8, 16
B.
1, 3, 5, 7
C.
5, 10, 15, 25
D.
3, 6, 9, 12
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Solution
An arithmetic progression has a constant difference between consecutive terms. The sequence 1, 3, 5, 7 has a common difference of 2.
Correct Answer: B — 1, 3, 5, 7
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Q. Which of the following statements is true regarding an arithmetic progression?
A.
The sum of any two terms is constant.
B.
The difference between consecutive terms is constant.
C.
The product of any two terms is constant.
D.
The ratio of any two terms is constant.
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Solution
In an arithmetic progression, the difference between consecutive terms is constant, which is the defining property of an AP.
Correct Answer: B — The difference between consecutive terms is constant.
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