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Previous Year Boards Questions, Chapter 5 - Arithmetic Progressions, , , , , , 1 Mark:, 1. Find the 17th term from the end of the AP: 1,6, 11, 16 ......211,216. CBSE Sample Paper 2017, 2, Whatis the common difference of an A.P, in which a2, — a, = 84? Mathematics 2017 (30/1), 3. Find the tenth term of the sequence V7, VB, VTS, ... ... CBSE Sample Paper 2016, 4. For what value of k will the consecutive terms 2k + 1,3k + 3 and 5k ~ 1 form an AP.?, 2016, Foreign (30/2/1), 5. Find the 9° term from the end (towards the first term) of the A.P. 5,9,13, 185., SSE 2016, Delhi (30/1/1), 6. For what value of k will k + 9, 2k — 1 and 2k + 7 are the consecutive terms of an A.P.?, CBSE 2016, Outside Delhi (30/1), 7. Ifthe common difference of an AP ts 3, then what is a,, — a,?. CBSE Sample Paper 2015, 8. Find the 25" term of the AP. —5, 2015, Foreign (30/2/1), 9. Ifk,2k — 1 and 2k + 1 are three consecutive terms of an AP’., the value of k is, A) 2 B) 3 cq -3 D) 5, 2014 (30/1), (30/2), (30/3), 10. The common difference of the aps. see ww IS CBSE 2013, Delhi (30/1/1), ADP B) -p c) -1 da, 11. Ifthe n™ term ofan A. P. is (2n + 1), then the sum of its first three terms is, A) 6n43 B) 15 c) 12 D) 21, 2012, Outside Delhi (30/1), 12. The next term of the A P. ¥16, y50, V6, ...is 2012, Foreign (30/2/1), A) 46 B) 128 ©) vi6z pb) V200, 13. The sum of first 20 odd natural numbers is: CBSE 2012, Delhi (30/1/1), A) 100 B) 210 c) 400 D) 420, 14, Ifthe common difference of an A.P, is 3, then azy — ais is 2011 Outside Delhi (30/1), A) S B) 3 C) 15 D) 20, 15. The value of aj, — a9 for the A.P. 2, 7, 12, 17, is 2011, Foreign (30/2/1), A) 100 RB) 10 Cc) 50 D) 20, 16. Inan AP, ifd = —2,n = 5 and a, = 0, then the value of ais CBSE 2011, Delhi (30/1/1), A) 10 B) 5 C) -8 D) 8, 17. Ifthe sum of first m terms of an A.P. is 2m? + 3m, then what it its second term?, 2010, Foreign (30/2/1), 18. Ifthe sum of first p terms of an AP., is ap? + bp, find its common difference., , 2010, Delhi (30/1/1)

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19. If ‘, a@,2 are three consecutive terms of an AP,, then find the value of a., 2009, Outside Delhi (30/1), 20, For what value of k, are the numbers x, 2x + k and 3x + 6 three consecutive terms of an A.P.?, 2009, Foreign (30/2/1), 21, For what value of p, are 2p — 1,7 and 3p three consecutive terms of an A.P.?, CBSE 2009, Delhi (30/1/1), 22. The first term of an AP. is p and its common difference is g. Find its 10" term., 2008 (30/2/1), (30/2/2), (30/2/2), 23. Which term of the sequence 114, 109, 104, .. is the first negative term? CBSE Sample Paper I 2008, 2 Marks:, 1. Find the sum of all natural numbers that are less than 100 and divisible by 4., CBSE Sample Paper 2017, 2. If seven times the 7* term of an A.P. is equal to eleven times the 11% term, then what will be its 18°, term? CBSE 2017, Foreign (30/2/1), 3. Find how many integers between 200 and 500 are divisible by 8. CBSE 2017, Delhi (30/1/1), 4. Which term of the progression 20,19 mm 18, 17; . is the first negative term?, 2017, Outside Delhi (30/1), 5. How many two digit numbers are divisible by 7? CBSE Sample Paper 2016, 6. If the ratio of sum of the first m and n terms of an AP. is m* : n*, show that the ratio of its m" and, n'* terms is (2m — 1): (2n — 1). 2016, Foreign (30/2/1), 7. How many terms of the AP. 18, 16, 14, ..... be taken so that their sum is zero?, CBSE 2016, Delhi (30/1/1), 8. The 4" term of an AP_ is zero. Prove that the 25" term of the A-P. is three times its 11" term., 2016, Outside Delhi (30/1), 9, Find the 4 term from the end of the AP. - 11, —B, = 5, .....0.,49, CBSE Sample Paper 2015, 10. In an AP, if S, + S; = 167 and S,, = 235, then find the AP, where S,, denotes the sum of its first n, terms. CBSE 2015, Outside Delhi (30/1), 11, The fourth term of an AP, is 11, The sum of the fifth and seventh terms of the AP. is 34, Find its, common difference. 2015, Foreign (30/2/1), 12. Find the middle term of the A.P. 6, 13, 20, ..., 216. CBSE 2015, Delhi (30/1/1), 13. Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5., 2014 (30/1), (30/2), (30/3), 14. How many three-digit natural numbers are divisible by 7? CBSE 2013 Delhi (30/1/1), 15. How many two-digit numbers are divisible by 3?. CBSE 2012, Outside Delhi (30/1), 16. Inan AP, the first term is 12 and the common difference is 6. If the last term of the A.P. is 252, find its, middle term. 2012, Foreign (30/2/1), 17, Find the sum of all three digit natural numbers, which are multiples of 11,, , CBSE 2012, Delhi (30/1/1)

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18. Find how many two-digit numbers are divisible by 6. CBSE 2011, Outside (30/1), 19. Find whether —150 is a term of the AP 17,12,7,2, .. 2 CBSE 2011, Delhi (30/1/1), 20. Inan AP, the first term is —4, the last term is 29 and the sum of all its terms is 150, Find its common, difference. 2010 Foreign (30/2/1), 21, Inan AP, the first term is 2, the last term is 29 and sum of the terms is 155, Find the common difference, of the A. P_ 2010 Delhi (30/1/1), 22. Which term of the AP. 3, 15, 27, 39, ... will be 120 more than its 21“ term?, 2009 Outside Delhi (30/1), 23. The 17% term of an AP. exceeds its 10" term by 7. Find the common difference., CBSE 2009 Foreign (30/2/1), 24. IfS,, the sum of first n terms of an AP. is given by S,, = 3n® — 4n, then find its nth term., CBSE 2009 Delhi (30/1/1), 3 Marks:, 1. The sum of first six terms of an A.P_ is 42. The ratio of its 10" term to its 30 term is 1: 3. Find the, first term of the A.P. CBSE Sample Paper 2017, 2. Find the sum of the following series:, 5+ (—41) +9 + (—39) + 13 + (—37) + 17 + + (—5) + 81 + (—3). 2017, Foreign (30/2/1), 3. ifm" term of an AP. is*and né” term is = then find the sum of its first mn terms,, CBSE 2017, Delhi (30/1/1), 4. Find the sum of m terms of the series (4~+) + (4-2)+(4-2)+~, n x, CBSE 2017, Delhi (30/1/1), 5. The first term of an AP. is 5, the last term is 45 and the sum of all its terms is 400. Find the number of, terms and the common difference of the AP., 2017, Outside Delhi (30/1), 6. Inan AP, the sum of first n terms is + = Find the 25% term, CBSE Sample Paper 2016, 7. The ninth term of an AP. is equal to seven times the second term and twelfth term exceeds five times, the third term by 2. Find the first term and the common difference. CBSE Sample Paper 2016, 8. Divide 56 in four parts in AP_ such that the ratio of the product of their extremes (1* and 4%) to the, product of means (2™ and 3°) is 5: 6. CBSE 2016, Foreign (30/2/1), 9. Ifthe sum of first 7 terms of an AP, is 49 and that of its first 17 terms is 209, find the sum of first n, terms of the AP. CBSE 2016, Delhi (30/1/1), 10. If the ratio of the sum of first n terms of two A.l’s is (7n + 1) : (4n + 27), find the ratio of their m', terms. E 2016, Outside Delhi (30/1), 11. Find the sum of the two middle most terms of the AP, CBSE Sample Paper 2015, 12. The 14" term of an AP is twice its 8 term. Ifits 6“ term is —8, then find the sum of its first 20 terms,, , 2015, Outside Delhi (30/1)

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13., , 14., , 16,, , 17., , 18., , 19., , 20., 21,, , 22., , 23., , 24,, , 2s., , 26., , 27., , 28., , 29,, , 30., , 3L, , 32., , InanA.P, if the 12" term is —13 and the sum of its first four terms is 24, find the sum of its first ten, , , , terms. 2015, Foreign (30/2/1), If S,, denotes the sum of first n terms of an AP, prove that $,. = 3(S — S,)2015, Delhi (30/1/1), ‘The sum of the first seven terms of an AP is 182. If its 4" and the 17” terms are in the ratio 1:5, find, the AP. 2014, Outside Delhi (30/3), ‘The sum of the 24 and the 7® terms of an AP is 30. If its 15“ term is 1 less than twice its 0% term, find, the AP. 2014, Outside Delhi (30/2), ‘The sum of the S® and the 9" terms of an AP is 30, If its 25" term is three times its 8 term, find the, AP. 2014, Outside Delhi (30/1), Find the number of terms of the AP 18,15 :, 13, oss .0, =49 = and find the sum of all its terms., 2013, Delhi (30/1/1), Find the sum of all multiples of 7 lying between 500 and 900., CBSE 2012, Outside Delhi (30/1), Find the sum of first 40 positive integers divisible by 6. 2012, Foreign (30/2/1), If 4 times the fourth term of an A. P. is equal to 18 times its L8* term, then find its 22> term., 2012, Foreign (30/2/1), ‘The 17th term of an AP is 5 more than twice its 8th term. Ifthe 11th term of the AP is 43, then find the, nth term. CBSE 2012, Delhi (30/1/1), Find an AP. whose fourth term ts 9 and the sum of its sixth term and thirteenth term is 40., 2011, Outside Delhi (30/1), Find the sum of first n terms ofan A.P. whose n™ term is Sn — 1, Hence find the sum of first 20 terms., 2011, Foreign (30/2/1), Find the value of the middle term of the following AP, —6,-2,2,... ..,58. CBSE 2011, Delhi (30/1/1), Determine the AP whose fourth term is 18 and the difference of the ninth term from the fifteenth term., is 30. 2011, Delhi (30/1/1), ‘The sum of the first sixteen terms of an A.P. is 112 and the sum of its next fourteen terms is 518, Find, the AP. 2010, Foreign (30/2/1), In an A.P,, the sum of first ten terms is —150 and the sum of its next ten terms is —550. Find the A.P,, E 2010, Delhi (30/1/1), , ‘The sum of first six terms of an arithmetic progression is 42, The ratio of its 10 term to its 30% term, is 1 = 3. Calculate the first and the thirteenth term of the A. P., CBSE 2009, Outside Delhi (30/1), 1f9 term of an A.P_is zero, prove that its 29" term is double of its 19% term., 2009, Foreign (30/2/1), The sum of 4th and 8th terms of an AP. is 24 and sum of 6th and 10th terms is 44, Find A.P., CBSE 2009, Delhi (30/1/1), ind 3, 10,17 ... equal?, 2008 (30/2/1), (30/2/2), (30/2/3), , For what value of n are the nth terms of two A.P.s 63, 65, 67,

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33., , 34., , 35., , If'm times the mth term of an AP. is equal to n times its nth term, find the (m + n)th term of the AP., 2008 (30/2/1), (30/2/2), (30/2/3), , Inan AP,, the first term is 8, nth term is 33 and sum to first n terms is 123. Find n and d, the common, , difference CBSE 2008, Foreign (30/2/1), , A contract on construction job specifies a penalty for delay of completion beyond a certain date as, follows: Rs. 200 for Ist day,, Rs. 250 for second day, Rs. 300 for third day and so on. If the contractor, pays Rs. 27750 as penalty, find the number of days for which the construction work ts delayed., , CBSE Sample Paper 2008, , 4 marks:, , 10., , A manufacturer of TV sets produced 600 units in the 3~! year and 700 units in the 7% year. Assuming, that, production increases uniformly by a fixed number of units every year. Find, , 1. The production in 1* year., IL The production in LO“ year., Ill. The total production in 7 years. CBSE Sample Paper 2017, , 1f1+4474 10 +++ x = 287, find the value of x. CBSE 2017, Foreign (30/2/1), , A child puts one five-rupee coin of her saving in the piggy bank on the first day. She increases her, saving by one five-rupee coin daily. If the piggy bank can hold 190 coins of five rupees in all, find the, number of days she can continue to put the five-rupee coins into it and find the total money she saved., Write your views on the habit of saving, CBSE 2017, Foreign (30/2/1), , ‘The ratio of the sums of first m and firstn terms ofan AP_is m? : n?. Show that the ratio of its m* and, n® terms is (2m = 1) + (2n = 1). 2017, Delhi (30/1/1), , If the ratio of the sum of the first n terms of two APs is (7m + 1): (4n + 27), then find the ratio of, their 9 terms. CBSE 2017, Outside Delhi (30/1), , The minimum age of children to be eligible to participate in a painting competition is 8 years. It is, observed that the age of youngest boy was 8 years and the ages of rest of participants are having a, common difference of 4 months. If the sum of ages of all the participants is 168 years, find the age of, eldest participant in the painting competition. CBSE Sample Paper 2016, , Reshma wanted to save at least t 6,500 for sending her daughter to school next year (after 12 months)., She saved 3 450 in the first month and raised her saving by 2 20 every next month. How much will she, be able to save in next 12 months? Will she be able to send her daughter to the school next year? What, value is reflected in this question? 2016, Foreign (30/2/1), , A thief runs with a uniform speed of 100 m/minute. After one minute a policeman runs after the thief, , to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by, , 10 m/minute every succeeding minute. After how many minutes the policeman will catch the thief., CBSE 2016, Delhi (30/1/1), , ‘The house in a row are numbered consecutively from 1 to 49. Show that there exists a value of X such, that sum of numbers of houses preceeding the house numbered X is equal to sum of the numbers of, houses following X. 2016, Outside Delhi (30/1), , Yasmeen saves Rs.32 during the first month, Rs.36 in the second month and Rs.40 in the third month., If she continues to save in this manner, in how many months she will save Rs.2000, which she has, intended to give for the college fee of her maid's daughter. What value is reflected here., , CBSE Sample Paper 2015