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Maharashtra SSC Algebra HOTS Questions with Answers – Arithmetic Progression | Class 10 Board Exam 2027

Practice set · 1 hr · 65 marks · for SSC 10th and similar exams

2027 60 minutes 65 marks Save WhatsApp

Sections

Most repeated board questions (2024–2026) 12 Q
HOTS: likely questions for 2027 14 Q

About this HOTS set

Students call the most important, most-likely-to-come questions of a chapter its HOTS or IMP questions. This page collects them for Arithmetic Progression (Maharashtra SSC Class 10 Algebra) for the 2027 board exam. Part 1 has the questions the board has actually repeated in its recent papers; Part 2 has new questions in the same board style, covering the patterns that keep coming back and the parts of the chapter not yet asked, with a few harder thinking-type questions.

The board questions are taken from the official MSBSHSE SSC Algebra question papers of March 2024, July 2024, March 2025, July 2025, March 2026 and June 2026. All step-by-step answers and all the new questions are written by Doubtly.

Marks from this chapter in recent board papers

Board paperMarks (including internal options)
March 20248
July 20248
March 20258
July 20259
March 20268
June 20268

Question types that repeat most

  • 1-mark: first term and common difference of a given A.P., or \(t_1\) from a formula like \(t_n = 3n - 2\).
  • 2-mark: \(n\)th term of an A.P. The 19th term of 7, 13, 19, 25, … came in three papers (March 2024, July 2024, March 2025).
  • “Which term is …?” and “how many numbers are divisible by …” activities.
  • 3-mark activity on three consecutive terms \(a - d\), \(a\), \(a + d\).
  • A 3- or 4-mark money word problem in five of the six papers (instalments, savings, simple interest, loan repayment), usually solved with \(S_n\).

Exam tips

  • Write the given data (\(a\), \(d\), \(n\), \(t_n\) or \(S_n\)) in one line before using any formula.
  • Learn both sum formulas: \(S_n = \dfrac{n}{2}[2a + (n - 1)d]\) and \(S_n = \dfrac{n}{2}(t_1 + t_n)\); use the second when the last term is known.
  • In money problems, check if the payment decreases (then \(d\) is negative) and whether the month has 28, 29, 30 or 31 days.
  • If \(S_n\) gives a quadratic in \(n\), reject answers that are negative or not whole numbers.

Chapters covered

Instructions

Solve on paper with a timer, then check against the solutions.

Most repeated board questions (2024–2026)

  1. Asked in: July 2024 and June 2026 board papers (exactly the same A.P.)

    Find the first term and common difference for the following A.P. : 5, 1, –3, –7, ……

    1 mark See answer →

  2. Asked in: March 2024 board paper; March 2025 asked the same with \(t_n = 3n - 4\)

    Find first term of the sequence \(t_n = 3n - 2\).

    1 mark See answer →

  3. Asked in: March 2024 board paper

    For an A.P., \(t_7 = 4\), \(d = -4\), then \(a\) = ____ .

    1. (A) 6
    2. (B) 7
    3. (C) 20
    4. (D) 28
    1 mark See answer →

  4. Asked in: March 2024, July 2024 and March 2025 board papers (exactly the same A.P.); March 2026 asked the 24th term of 12, 16, 20, 24, …

    Find the 19th term of the following A.P. : 7, 13, 19, 25, ……

    2 marks See answer →

  5. Asked in: July 2025 board paper

    Which term of the following A.P. is 560 ? 2, 11, 20, 29, ……

    2 marks See answer →

  6. Asked in: July 2025 board paper

    In an A.P. sum of three consecutive terms is 27 and their product is 504. Complete the following activity to find the terms.

    Activity :
    Let three consecutive terms be \(a - d\), \(a\), \(a + d\).
    \(\therefore a - d + a + a + d = \) ____
    \(\therefore a = \) ____
    Similarly : \((a - d) \times a \times (a + d) = \) ____
    \(\therefore [(9)^2 - d^2] \times 9 = 504\)
    \(\therefore (81 - d^2) \times 9 = 504\)
    \(\therefore d^2 = 81 - \) ____
    \(\therefore d = \pm 5\)
    Thus by putting \(a = 9\) and \(d = 5\) we get three consecutive terms = ____
    Or by putting \(a = 9\) and \(d = -5\) we get three consecutive terms = ____

    3 marks See answer →

  7. Asked in: June 2026 board paper

    Complete the following activity to find, ‘how many three digit natural numbers which are divisible by 5’.

    Activity :
    Three digit natural numbers divisible by 5 are as follows : 100, 105, 110, ……, 995.
    \(t_n = \) ____, \(a = \) ____, \(d = 5\), \(n = ?\)
    \(t_n = a + (n - 1)d\) …… formula
    \(995 = \) ____ \(+ (n - 1) \times \) ____
    \(895 = (n - 1) \times 5\)
    \(\dfrac{895}{5} = n - 1\)
    ____ \(+ 1 = n\)
    ____ \(= n\)
    \(\therefore\) There are 180 three digit natural numbers, divisible by 5.

    3 marks See answer →

  8. Asked in: March 2026 board paper

    Sachin invested some amount in a National Saving Certificate Scheme. In the first year he invested ₹ 5,000, in the second year ₹ 7,000, in the third year ₹ 9,000 and so on. Find the total amount that he invested in 12 years.

    3 marks See answer →

  9. Asked in: March 2025 board paper

    A farmer borrows ₹ 1,000 and agrees to repay with a total interest of ₹ 140, in 12 instalments. Each instalment being less than the preceding instalment by ₹ 10. What should be the amount of his first and last instalment ?

    4 marks See answer →

  10. Asked in: July 2024 board paper

    ₹ 2,000 is invested at 10 percent simple interest. Check at the end of the every year whether the interest amount is in A.P. or not. If this is an A.P., then find interest amount after 10 years.

    4 marks See answer →

  11. Asked in: March 2024 board paper

    In a ‘Mahila Bachat Gat’ Kavita invested from the first day of month ₹ 20 on first day, ₹ 40 on second day and ₹ 60 on third day. If she saves like this, then what would be her total saving in the month of February 2020 ?

    4 marks See answer →

  12. Asked in: June 2026 board paper

    Ajay Sharma repays the borrowed amount of ₹ 3,25,000 by paying ₹ 30,500 in the first month and then decreases the payment by ₹ 1,500 every month. How long will it take to clear his amount ?

    4 marks See answer →

HOTS: likely questions for 2027

  1. Which of the following sequences is an A.P.?

    1. (A) 1, 4, 9, 16, …
    2. (B) 2, 4, 8, 16, …
    3. (C) −3, −1, 1, 3, …
    4. (D) \(1, \dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{4}, \ldots\)
    1 mark See answer →

  2. For an A.P., \(a = 6\) and \(d = -2\). Then \(t_5 = \) ____.

    1. (A) 14
    2. (B) −2
    3. (C) −4
    4. (D) 2
    1 mark See answer →

  3. The sum of the first 20 natural numbers is ____.

    1. (A) 200
    2. (B) 190
    3. (C) 220
    4. (D) 210
    1 mark See answer →

  4. Find the common difference of the A.P. whose \(n\)th term is \(t_n = 7 - 4n\).

    1 mark See answer →

  5. If \(2k + 1\), 13, \(5k - 3\) are three consecutive terms of an A.P., find \(k\).

    1 mark See answer →

  6. Find the 15th term from the end of the A.P. 3, 8, 13, …, 253.

    2 marks See answer →

  7. Find the sum of the first 25 terms of the A.P. 2, 5, 8, 11, ……

    2 marks See answer →

  8. Complete the following activity to find the sum of all two-digit odd natural numbers.

    Activity :
    Two-digit odd numbers are 11, 13, 15, ……, 99.
    \(a = \) ____, \(d = 2\), \(t_n = \) ____
    \(t_n = a + (n - 1)d\)
    \(99 = 11 + (n - 1) \times 2 \Rightarrow n = \) ____
    \(S_n = \dfrac{n}{2}(t_1 + t_n) = \dfrac{\text{____}}{2}(11 + 99) = \) ____

    3 marks See answer →

  9. In an A.P., the 4th term is 15 and the 9th term is 35. Find the first term, the common difference and the 20th term.

    3 marks See answer →

  10. How many terms of the A.P. 24, 21, 18, … must be taken so that their sum is 78? Explain why there are two answers.

    3 marks See answer →

  11. The sum of the first \(n\) terms of an A.P. is \(S_n = 3n^2 + 5n\). Find the A.P. and its \(n\)th term.

    3 marks See answer →

  12. Riya saves ₹ 50 in the first week and increases her saving by ₹ 10 every week. In how many weeks will her total saving become ₹ 2,900?

    4 marks See answer →

  13. A school has ₹ 1,600 to give 8 cash prizes to students. Each prize is ₹ 30 less than the prize before it. Find the value of each prize.

    4 marks See answer →

  14. Find the sum of all three-digit natural numbers which leave remainder 3 when divided by 7.

    4 marks See answer →