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ARITHMETIC PROGRESSION, Show that each of the progressions given below is an AP. Find the first term, common, diference and next term of each., , (i) 9, 15, 21, 27,.... .., , (i) 11,6, 1,-4,.., , ci)-1, , *******, , ) 78,8, 2,, , 20,45,80, 125., Find:, , i) the 20th term of the AP 9,13,17,21, , *, , (i) the 35h term of AP 20,17,14,1 1,., (ii) the 18h term of the AP 2,V18,50, 98,., (iv) the 9h term of the, (v) the, , 15the term, , Find the 37P m, , Find the, , 25, , AP, , *******, , 35 79, 144*, , ofthe AP40,-15,10,35,., , oftheAP6.7, , term, , of the APS,44,3.3,., , Find the nth term of each of the following Aps:, , i)5,11, 17, 23, , . ., , (i) 16,9,2,-5,, , If the nth tem of a progression is (4n- 10) show that it is an AP. Find its, , () first term, (ii) common difference (ii) 16 the term., , How many terms are there in the AP 6,1 0, 14, 18,.., 174?, , How many terms are there in the AP 41, 38, 35,..8?, , How many tems are there in the AP, , 18,15,13,.47.?, , Which term of term of the AP 3,8,13,18,... is 88?

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Which term of AP 72,68,64,60,.. is 0?, , Which term of the AP, , Which term of the AP 21, 18, 15, .... i5 -81?, , Which term of the AP 3,8, 13,18,.... Will be 55 more than its 20h term?, , Which tem of the AP 5, 15, 25,.. will be 130 more than its 31 term?, , If the 10th term of an AP is 52 and 17h term is 20 more than its 13h tem, find the AP, , Find the middle term of the AP 6, 13, 20,216., , Find the middle term of the AP 10,7, 4,., , (-62)., , Find the8th term from the end of the AP 7, 10, 13,., , 184., , Find the 6th tem form the end of the AP 17, 14, 11, ..(40)., , Is 184 a tem of the AP 3, 7, 11, 15,..?

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Is-150 a term of the AP11,8,5,2,..?, , Which term of the AP 121, 117, 113,.. is its first negative term?, 12, , Which term of the AP 20,19, , Is the first negatve term?, , The 7th term of the an AP is -4 and its 13th tem is -16. Find the AP., , The 4th term of an AP is zero. Prove that its 25th tem is triple its 11th tem., , The 8th term of an AP is zero. Prove that its 38th term is triple its 18th tem., , The 4th term of an AP is 11. The sum of the 5h and 7th terms of this AP is 34. Find its, common difference, , The 9h tem of an AP is-32 and the sum of its 11h and 13h terms is -94. Find the common, difference of the AP., , Detemine the nth term of the AP whose 7th term is -I and 16 term is 17., , If4 times the 4th tem ofan AP is equal to 18 times its 18h tem then find its 22md tem., , If 10 times the 10th term of an AP is equal to IS times the 15h term, show that its 25th term, IS Zero.

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The 17th tem of AP is 5 more than twice its 8th term. If the 11h term of the AP is 43, find, its nth term., , How many three-digit numbers are divisible by 9?, , Determine k so that (3k -2). (4k - 6) and (k +2) are three consecutive terms of an AP, , Find the value of x for which the numbers (5x + 2), (4x- I) and (x+2) are in AP., , If(3y 1), (3y, , +, , ofy., , 5) and (5y + 1) are three consecutive terms of an AP then find the value, , Find the value of x for which (x +2), 2x, ()2x +, , 3) are three consecutive terms of an AP, , Show that (a-b) (a +*) and (a +6*)are in AP., , If k(2k-1) and (2k+1) are the three successive terms of an AP, find the value of k., , Find the sum of the first n natural numbers., , Find the sum of first n even natural numbers., , Ifa,2, , are, , in, , AP,, , find the value ofa.

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If(2p +1). 13, (5p-3) are in AP, find the value of p., , if(2p-1).7, 3p are in AP, find the value ofp., , Ifthe sum of first n terms is (3n, , +5n), find its common difference., , Find an AP whose 4th tem is 9 and the sum of its 6th and 13 terms is 40., , The common diference of the AP, , ., , IS, , (o) p b)-pc)-1d)1, Answer: (o)-1, , The common difference of the AP, , Answer: (d)-b, , The next term of the AP 7, J28,V63,.. is, , la)70 (b)84 te) 98(d)I12, Answer: (d), , 12, , f 4,7,72,28 are in AP then x, =?, (a) 19 (b) 23 (c) 22 (d) cannot be determined, Answer: (c) 22, , If the nth term of an AP is (2n+ 1) then the sum of its first three terms is, (a) ónt3 (b) 15 (¢) 12 (d) 21, Answer: (b) 15, , The sum of first n terms of an AP is (3, , +6n).The common difference of the AP is, , (a) 6 (b) 9 (c) 15 (d)-3, , The sum of first n terms of an AP is(Sn-*). The nth term of the AP is

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The 13th tem of an AP is 4 times its 3d term. If its 5th tem is 16 then the sum of its first ten, terms is, (a) 150 (b) 175 (c) 160 (d) 135, Answer: (b) 175, , An AP 5, 12, 9, .., , has S0 terms. Its last term is, , (a) 343 (b) 353 (c) 348 (d) 362, Answer: (c) 348, , The sum of the first 20 odd natural numbers is, (a) 100 (b) 210 (c) 400 (d) 420, Answer: (c) 400, The sum of first 40 positive integers divisible by 6 is, (a) 2460 (b) 3640 (c) 4920 (d) 4860, Answer: (c) 4920, , How many two digit numbers are divisible by 3?, (a) 25 (b) 30 (¢) 32 (d) 36, Answer: (b) 30, How many three-digit number are divisible by 9?, (a) 86 (b) 90 (c) 96 (d) 100, Answer: (d) 100, , What is the common difference of an AP in which a-=32?, (a) 8 (b)-8 (c)4 (d) 4, Answer: (a)8, , lf a, denotes the nth term of the AP 3, 8, 13, 18,., , then what is the value of (o-42) ?, , (a) 40 (b) 36 () 50 (d) s6, , Answer: (C) 50, , Which term of the AP 72, 63, 54, .... is 0?, , (a)8th (b)9h (c) 10th (d)i1h, Answer: (b) 9th, , Which term ofthe AP 25, 20, 15,, , ..., , is the first, , (a) 10h (b) 9th (c) 8th (d) 7th, Answer: (d) 7h, , Which term ofthe AP 21,42, 63, 84,.. is 210?, , (a) 9h (b) 10 (c) 11th (d) 12h, Answer: (b) 10h, , negative tem?