Class 10 Exam > Class 10 Notes > Mathematics Class 10 ICSE > Worksheet: Arithmetic Progression
Worksheet: Arithmetic Progression | Mathematics Class 10 ICSE PDF Download
Section A – Very Short Answer Questions
Q1. Write the common difference of the AP: 12, 7, 2, −3, …
Q2. Find the 5th term of the AP: 4, 9, 14, …
Q3. If the 3rd term of an AP is 10 and 5th term is 18, find the common difference.
Q4. The 1st term of an AP is 7 and common difference is 0. Write the 4th term.
Q5. Find the arithmetic mean between 8 and 20.
Section B – Short Answer Questions (2–3 marks each)
Q6. Find the 12th term of the AP: 5, 11, 17, …
Q7. Which term of the AP: 15, 12, 9, … will be −6?
Q8. Find the sum of the first 25 terms of the AP: 7, 10, 13, …
Q9.The sum of first 15 terms of an AP is 630 and its first term is 7. Find the common difference.
Q10. Insert 4 arithmetic means between 3 and 23.
Section C – Long Answer Questions (4–5 marks each)
Q11. Find the sum of the first 30 multiples of 9.
Q12. The 7th term of an AP is 32 and 13th term is 62. Find the first term, common difference, and sum of first 20 terms.
Q13. A farmer arranges trees in rows. First row has 20 trees, second 18, third 16, and so on. If the arrangement continues until a row has 0 trees, find:
(i) The number of rows
(ii) The total number of trees
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FAQs on Worksheet: Arithmetic Progression - Mathematics Class 10 ICSE
| 1. What is an arithmetic progression (AP) and how is it defined? |  |
Ans.An arithmetic progression (AP) is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant difference is called the common difference (d). If 'a' is the first term and 'd' is the common difference, the n-th term of the AP can be expressed as a + (n-1)d.
| 2. How can we find the sum of the first n terms of an arithmetic progression? | |
Ans.The sum of the first n terms (Sₙ) of an arithmetic progression can be calculated using the formula Sₙ = n/2 × (2a + (n-1)d) or Sₙ = n/2 × (first term + last term). Here, 'a' is the first term, 'd' is the common difference, and 'n' is the number of terms.
| 3. Can you provide an example of an arithmetic progression? | |
Ans.An example of an arithmetic progression is 2, 5, 8, 11, 14, ... In this sequence, the first term (a) is 2, and the common difference (d) is 3, as each term increases by 3 from the previous term.
| 4. What are some real-life applications of arithmetic progressions? | |
Ans.Arithmetic progressions have several real-life applications, including in finance for calculating interest, in construction for determining measurements, and in computer science for analyzing algorithms. They are also used in scheduling and planning, where regular intervals are needed.
| 5. How do you determine if a sequence is an arithmetic progression? | |
Ans.To determine if a sequence is an arithmetic progression, check if the difference between consecutive terms is the same throughout the sequence. If the difference remains constant, then the sequence is an AP. For example, in the sequence 4, 7, 10, 13, the differences (3) are constant, indicating it is an AP.
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