Class 10 Exam > Class 10 Notes > Mathematics (Maths) Class 10 > Unit Test: Arithmetic Progressions
Unit Test: Arithmetic Progressions | Mathematics (Maths) Class 10 PDF Download
Time: 1 hour
M.M. 30
Attempt all questions.
- Question numbers 1 to 5 carry 1 mark each.
- Question numbers 6 to 8 carry 2 marks each.
- Question numbers 9 to 11 carry 3 marks each.
- Question number 12 & 13 carry 5 marks each.
Q1: If a = 10 and d = 10, then first four terms will be: (1 Mark)
(a) 10, 30, 50, 60
(b) 10, 20, 30, 40
(c) 10, 15, 20, 25
(d) 10, 18, 20, 30
Q2: 11th term of the A.P. -3, -1/2, 2 …. is (1 Mark)
(a) 28
(b) 22
(c) -38
(d) -48
Q3: Which term of the A.P. 3, 8, 13, 18, … is 78? (1 Mark)
Q4: The 21st term of AP whose first two terms are -3 and 4 is: (1 Mark)
(a) 17
(b) 137
(c) 143
(d) -143
Q5: What is the common difference of an A.P. in which a21 – a7 = 84? (1 Mark)
Q6: The angles of a triangle are in A.P., the least being half the greatest. Find the angles. (2 Marks)
Q7: Find whether -150 is a term of the A.P. 17, 12, 7, 2, …? (2 Marks)
Q8: The 4th term of an A.P. is zero. Prove that the 25th term of the A.P. is three times its 11thterm. (2 Marks)
Q9: The 19th term of an AP is equal to three times its 6th term. If its 9th term is 19, find the A.P. (3 Marks)
Q10: If the seventh term of an AP is 1/9 and its ninth term is 1/7, find its 63rd term. (3 Marks)
Q11: The digits of a positive number of three digits are in A.P. and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (3 Marks)
Q12: A manufacturer of TV sets produced 800 sets in the third year and 1000 sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find: (5 Marks)
(i) the production in the 1st year
(ii) the production in the 10th year
(iii) the total production in the first 7 years
Q13: A sum of ₹1,600 is to be used to give ten cash prizes to students of a school for their overall academic performance. If each prize is ₹20 less than its preceding prize, find the value of each of the prizes. (5 Marks)
You can find the solutions of this Unit Test here: Unit Test (Solutions): Arithmetic Progressions
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FAQs on Unit Test: Arithmetic Progressions - Mathematics (Maths) Class 10
| 1. What is an arithmetic progression (AP)? |  |
Ans. An arithmetic progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference. For example, in the sequence 2, 5, 8, 11, the common difference is 3.
| 2. How can I find the nth term of an arithmetic progression? | |
Ans. The nth term of an arithmetic progression can be found using the formula: nth term = a + (n - 1)d, where 'a' is the first term, 'd' is the common difference, and 'n' is the term number you want to find.
| 3. What is the formula to calculate the sum of the first n terms of an arithmetic progression? | |
Ans. The sum of the first n terms of an arithmetic progression can be calculated using the formula: S_n = n/2 * (2a + (n - 1)d), where 'S_n' is the sum of the first n terms, 'a' is the first term, 'd' is the common difference, and 'n' is the number of terms to be added.
| 4. Can you give an example of a real-life application of arithmetic progressions? | |
Ans. One real-life application of arithmetic progressions is in calculating the total distance traveled in a series of evenly spaced intervals. For instance, if a person walks 2 meters in the first minute and increases their pace by 1 meter every subsequent minute, the distance they cover each minute forms an arithmetic progression.
| 5. How do you determine if a given sequence is an arithmetic progression? | |
Ans. To determine if a given sequence is an arithmetic progression, calculate the difference between consecutive terms. If the difference is constant throughout the sequence, then it is an arithmetic progression. If the differences vary, it is not an arithmetic progression.
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