Hard Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Write the 20th term of the A.P. whose first term is 3 and common difference is 7.
Perfect! Using the formula
(2) If
Correct! The first term is always
(3) What is the common difference of the A.P. whose
Excellent! Used the relationship between any two terms to find d.
(4) The 3rd and 7th terms of an A.P. are 10 and 26 respectively. Find the 1st term.
Perfect systematic approach to finding the first term!
Short Answer Questions (2 Marks Each)
Note: Answer each question with steps and explanation, in 2-3 sentences. Write down the answers on sheet and submit to the school subject teacher.
(1) Find the number of terms in the A.P. 7, 13, 19, ...., 301.
First term a =
Excellent! The A.P. has 50 terms.
(2) The sum of the first n terms of an A.P. is
Perfect! Used the relationship
(3) The sum of the first 12 terms of an A.P. is 420. If the first term is 10, find the common difference. d =
Excellent application of the sum formula!
(4) If 5 times the 5th term of an A.P. is equal to 3 times the 9th term, find the ratio of the 1st term to the common difference. a:d =
Perfect algebraic manipulation to find the ratio!
Long Answer Questions (4 Marks Each)
Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.
(1) The sum of first n terms of an A.P. is given by
10th term:
(2) A sum of ₹ 1000 is divided among three children in such a way that their shares are in A.P. and the product of the first and third share is 15,625. Find their individual shares. The shares are: ₹
Excellent problem involving A.P. with constraints!
(3) In an A.P., the sum of the first p terms is equal to the sum of the next q terms. Show that (2p + q - 1)d = -2a, where a is the first term and d is the common difference.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) The nth term of the A.P. 3, 6, 9, … is:
(a) 3n (b) 3n + 1 (c) 2n + 1 (d) 2n
Correct! First term a = 3, common difference d = 3, so
(2) If the sum of n terms of an A.P. is 4n +
(a) 5 (b) 4 (c) 1 (d) Cannot be determined
Correct! First term
(3) Which of the following A.Ps has a negative common difference?
(a) 8, 6, 4, 2 (b) 10, 20, 30 (c) 0, 0, 0 (d) 5, 7, 9
Correct! Common difference = 6 - 8 = -2 < 0.
(4) In an A.P., a = 4, d = -2, then
(a) -14 (b) -16 (c) -18 (d) -12
Correct!
(5) The sum of the first 20 terms of the A.P. 1, 3, 5, … is
(a) 400 (b) 200 (c) 420 (d) 380
Correct!
(6) Which term of the A.P. 25, 22, 19, … is zero?
(a) 9th (b) 10th (c) 11th (d) 12th
Correct! Setting
(7) If
(a) 29 (b) 30 (c) 31 (d) 17
Correct!
(8) In an A.P., a = -2, d = 5, find the sum of the first 15 terms.
(a) 505 (b) 520 (c) 540 (d) 555
Correct!
(9) In how many terms of the A.P. 5, 8, 11, … is the sum 450?
(a) 10 (b) 12 (c) 15 (d) 18
Correct! Using
(10) If the 3rd term of an A.P. is 8 and the 7th term is 20, what is the sum of the first 10 terms?
(a) 120 (b) 130 (c) 140 (d) 150
Correct! From given terms: d = 3, a = 2. Then
Arithmetic Progressions Challenge
Determine whether these statements about A.P.s are True or False:
Arithmetic Progressions Quiz
🎉 You Did It! What You've Learned:
By completing this worksheet, you now have a solid understanding of:
(1) A.P. Formula Mastery: Using
(2) Sum Calculations: Applying
(3) Term Relations: Finding unknown terms using given conditions
(4) Real-world Applications: Money distribution and practical A.P. problems
(5) Algebraic Manipulation: Proving relationships and deriving formulas
(6) Problem-solving Strategies: Working with constraints and multiple conditions
(7) Sequence Analysis: Identifying patterns and properties of arithmetic sequences
(8) Advanced Techniques: Using sum formulas to find individual terms
Excellent work mastering arithmetic progressions and their diverse applications!