Arithmetic Progressions: Class 10 Previous Year Questions

Arithmetic Progressions questions asked in CBSE board exams

Repeated questions first. Open the free app to see each question as it appeared in the paper, with its marking scheme.

1. n-1 20. Assertion (A) : The mean of first ·n' natural numbers is n(n + 1) Reason (R): The sum of first ·n' natural numbers is
   Board 20261 markAssertion-Reason
2. If the sum of first m terms of an AP is 2m2 + 3m, then its second term is : (A) 10 (B) 9 (C) 12 (D)
   Board 20251 markMCQ
3. Assertion (A) : Common difference of the AP : 5, 1, 3, Reason (R): Common difference of the AP : a1, a2, a3 an is obtained by d = an an 1.
   Board 20251 markAssertion-Reason
4. A sum of 2,000 is invested at 7% per annum simple interest. Calculate the interests at the end of 1st, 2nd and 3rd year. Do these interests form an AP ? If so, find the interest at the end of the 27th year.
   Board 20253 marksshort answer
5. If the roots of equation ax? + bx + c = O, a ± O are real and equal, then which of the following relation is true ? b2 b2 (a) (b) b²=ac (c) ac (d) In an A.P., if the first term a = 7, nth term an = 84 and the sum of first 2093 then n is equal to : n terms Sn 2…
   Board 20241 markMCQ
6. (A) The sum of first and eighth terms of an A.P. is 32 and their product is 60. Find the first term and common difference of the A.P. Hence, also find the sum of its first 20 terms. OR (B) In an A.P. of 40 terms, the sum of first 9 terms is 153 and the sum of …
   Board 20245 markslong answer
7. (a) The ratio of the 11th term to 17th term of an A.P. is 3 : 4.Find the ratio of 5thtermto 2lsttermof the sameA.P.Also,find theratioof the sum of first 5 terms to that of first 21 terms. OR (b) 250 logs are stacked in the following manner : 22logsinthebottom …
   Board 20235 markslong answer
8. How many terms of the arithmetic progression 45, 39, 33, ........ must be taken so that their sum is 180 ? Explain the double answer.
   Board 20235 markslong answer
9. (a) Find the sum of first 30 terms of AP : 30, 24, 18, ..... . 2 OR (b) In an AP if Sn = n (4n + 1), then find the AP.
   Board 20221 markvery short
10. Find the sum of first 20 terms of an A.P. whose nth term is given as a, = 5 - 2n.
    Board 20221 markvery short
11. In Mathematics, relations can be expressed in various ways. The matchstick patterns are based on linear relations. Different strategies can be used to calculate the number of matchsticks used in different figures. One such pattern is shown below. Observe the p…
    Board 20221 markvery short
12. Which term of the A.P. 49 2. (a) OR (b) Find a and b so that the numbers a, 7, b, 23 are in A.P. 3. , 4·-BBC, OPADAOP=60°,C 60° 3sfa-1 AABO400 , ZBAYZAOB1
    Board 20221 markvery short
13. Two APs have the same common difference. The first term of one of these is –1 and that of the other is – 8. Then the difference between their 4th terms is (a) -1 (b) -8 (c) 7 (d) -9
    CBSE practice 2023-241 markMCQ
14. Answer the questions based on the given information. In space exploration missions, ion propulsion engine is an efficient way of travelling. The first such engine was used in Deep Space 1 spacecraft. It produced a constant acceleration. Given below are approxi…
    CBSE practice 2022-234 markscase-based

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