Q.1 (B)(ii) Find the first term and common difference of the given A.P. 5, 1, –3, –7, ……
Arithmetic Progression
Arithmetic Progression
Every question from past board papers on Arithmetic Progression, newest paper first. Open any question for its full worked answer.
Maharashtra SSC Algebra (Mathematics Part I) Board Paper June 2026
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Q.3 (A)(ii) 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.
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Q.4 (iii) 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 ?
Maharashtra SSC Algebra (Mathematics Part I) Board Paper March 2026
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Q.1 (A)(iv) Sum of first five multiples of 3 is ....................... .
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Q.2 (A)(ii) Write the correct number in the given boxes from the given A.P. : 70, 60, 50, 40, ............
Here \(t_1 =\) ____, \(t_2 = 60\), \(t_3 =\) ____
\(\therefore a =\) ____, \(d =\) ____ -
Q.2 (B)(iv) Given A.P. is 12, 16, 20, 24, .................... Find the 24th term of this progression.
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Q.3 (B)(ii) 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.
Maharashtra SSC Algebra (Mathematics Part I) Board Paper March 2025
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Q.1 (A)(iii) Find the common difference of the following A.P. : 4, 4, 4, ...
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Q.1 (B)(ii) Find the first term of the given sequence : \(t_n = 3n - 4\).
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Q.2 (B)(iii) Find the 19th term of the following A.P. : 7, 13, 19, 25, ...
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Q.4 (ii) 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 ?
Maharashtra SSC Algebra (Mathematics Part I) Board Paper July 2025
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Q.1 (A)(iii) For given A.P. \(a = 3.5\), \(d = 0\), then \(t_2\) = .........................
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Q.2 (B)(iii) Which term of the following A.P. is 560 ?
2, 11, 20, 29, .......
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Q.3 (A)(i) 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 = ____
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Q.5 (ii) If first term of an A.P. is ‘\(p\)’, second term is ‘\(q\)’ and last term is ‘\(r\)’, then show that the sum of all terms is \(\dfrac{(p + r)(q + r - 2p)}{2(q - p)}\).
Maharashtra SSC Algebra (Mathematics Part I) Board Paper July 2024
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Q.1 (A)(iii) The sequence –10, –6, –2, 2, ............... .
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Q.1 (B)(ii) Find the first term and common difference for the following A.P. : 5, 1, –3, –7, ..................
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Q.2 (B)(iii) Find the 19th term of the following A.P. : 7, 13, 19, 25, ..........
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Q.4 (ii) ₹ 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.
Maharashtra SSC Algebra (Mathematics Part I) Board Paper March 2024
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Q.1 (A)(iii) For an A.P., \(t_7 = 4\), \(d = -4\), then \(a\) = .........................
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Q.1 (B)(ii) Find first term of the sequence \(t_n = 3n - 2\).
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Q.2 (B)(iii) Find the 19th term of the following A.P. :
7, 13, 19, 25, .......
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Q.4 (iii) 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 ?