LAST TIME REVISION ARITHMETIC PROGRESSION

1) The rth term of an AP is n and it's nth term is r; show that its mth term is r+ n- m.

2) If the 1st term of an AP is 34 and 6th term is 48, then find 2nd, 3rd, 4th and 5th term of the AP.    36.8,39.6,42.4,45.2

3) Find the middle term (or terms) and the sum of the following arithmetic series:
3+7+11+15+....+95.       1176

4) The fifth term of an AP is 30 and its twelfth term is 65, find the sum of its 20 terms.    1150

5) The sum of n terms of an AP is 3n²+ 5n. Find the number of the term which is equal to 152.        25

6) How many terms of the series {22+ 18+ 14+ 10 +....} must be added to get the sum 64 ? Explain the double answer.    4 or 8

7) The nth term of an AP is p; show that , the sum of its first (2n -1) terms is (2n -1)p.

8) Insert 7 arithmetic mean between 1 and 41.     6,11,16,21,26,31,36

9) Find the sum of all natural number between 500 and 1000 divisible by 13.     28405

10) a,b,c,d be respectively the sums of p, q, r terms of an AP , show that, a/p (q -r)+ b/q (r - p)+ c/r (p - q)=0

11) The sum of p terms of two AP 's are in the ratio (2 p + 1): (2p - 1). Find the ratio of their 8th terms.      31/29

12) The sum of three numbers in AP is 12 and the sum of their squares is 56; find the numbers.          2,4,6 or 4,6,2

13) The sum of four numbers in AP is 24 and product of the squares of extremes is 729; find the numbers.      3,5,7,9 or 6-3√7,6-√7, 6+√7, 6+3√7

14) There are n arithmetic means between 14 and 38 such that, second means: last means= 4:7; find n.         8 or 7

15) The base of a right angled triangle is 12cm and the three sides are in AP. Find the length of the hypotenuse.       20cm, 15cm

16) A man borrows Rs840 and agree to repay with a total interest of Rs240 in 12 installments , each installment being less than the preceding one by Rs8. What should be his first installment ?          Rs134

17) The cost of constructing a 500 metre road is as follows: Rs 22 for the first metre and an additional Rs2 for every subsequent metre. Find the cost of constructing the last metre of the road and that for the entire road.           Rs260500

18) The 10th term of an is - 15 and 31st term is -57. Find the first term and common difference of the AP.     3,-2

19) If the Pth term of an arithmetic progression is q and the qth term is p, show that p+qth term is 0.

20) Let Tᵣ be the rth term of an AP. If m. Tₘ = n. Tₙ, then show that Tₘ₊ₙ=0.

21) Which term of the AP {7, 11, 15,19...} is 111 ?       27

22) Is 600 a term of the AP {2, 9 ,16, 23,...}?  give reason for your answer.   No

23) The third term of an AP is 7 and the 7th term is 2 more than 3 times the 3rd term. Find the first term, the common difference and the sum of the first 20 terms.   -1,4, 740

24) Which term of the series 4+0-4-8-.......is -392?      100

25) If the 1st term and 4th term of an AP are 1 and -50 respectively then find the second and third terms of the AP.    -16, -33

26) If the 3rd and 5th of an AP are 19 and 31 respectively, then find first, second, 4th, 5th terms of the AP.         7,13,25,31

27) Given a²+2a+2, 3a²+6a+6, 4a²+5a+4 are in AP, find the value or values of a.     -2 or -3

28) The nth term of an AP is 3n -1. Find the progression.      2,5,8,11...

29) The sum to n terms of an AP is n². Find the common difference.    2

30) Find the middle term (or terms) and the sum of each of the following series :
a) 2+ 5+8 + ....152.       77,3927
b) 1/2+ 1/3+ 1/6 +....(-5/6).     -1/6,-3/2
c) 2+ 2.4 +2.8+....10.4.           6,6.4,136.4
d) 1+5+9+....101.              49,53,1326

31) The 12th term of an AP is -13) and the sum of its first four terms is 24, find the sum of first 10 terms of an AP.     0

32) The 5th and 11th terms of an AP are 41 and 20 respectively. What is its first term? Find the sum of its first 11 terms.       55, 825/2

33) Show that the sum of n terms of the series {4+12+20+ 28+....} is the square of an even number.     

34) Prove that when 1 is added to the sum of n terms of the series {8+16+24+...}, the result will be a perfect square.         

35) Find the sum of the series 1+3+4+8 +7+13 +10+18 +....23 terms .      518

36) The three consecutive terms of an AP are x + 2, 4x-6 and 3x - 2. Find the terms.   5,6,7

37) The third term of an AP is 25 and 10th term is - 3. Find the first term and the common difference.       33,-4

38) The third term of an AP is 1/5 and the 5th term is 1/3. Show that the sum to 15 terms of an AP is 8.     

39) The sum of P terms of the series is 3P² + 5 P. Prove that terms of the series forms AP .     95

40) Find the 12th term of a series in AP , whose sum of n terms is 4n²+ 3n.    95

41) If 51+ 53 +55+.....tₙ=5151, then find the value of tₙ.         151

42) If the sum of the first n terms of an be n²+3n, which term of it has the value 162?     80

43) The nth term of an AP is 7n - 5; find the sum of first 20 terms of the series.      1370

44) How many terms of the series {27+ 24 +21 +....} must be added to get sum 132?    8 or 11

45) The first and the last term of an AP having finite number of terms are respectively -2 and 124 and the sum of the AP is 6161. Find the number of terms in the AP and also its common difference.     101, 1.26

46) How many even numbers are there between 91 and 259? Find also the sum of the even numbers between them.     84,14700

47) Find the sum of all multiples of 11 between 100 and 400.    6831

48) The sum of the three integers in AP 24 and their product is 440; find the integers.     5,8,11 or 11,8,5

49) The sum of the three integers in AP is 24 and the sum of their squares is 194, find the numbers.           7,8,9 or 9,8,7

50) The sum of 4 integers in AP is 20 and the sum of their squares is 120, find them.    2,4,6,8 or 8,6,4,2

51) Divide 32 into 4 parts which are in AP such that the ratio of product extremes to the product of means is 7:15.                 2,6,10,14 


52) Divide 21 into 3 parts in AP such that the product of the first of the second parts is 21.       3,7,11

53) Insert 5 arithmetic means between -19 and 23.       -12,-5,2, 9, 16

54) There are n arithmetic means between 4 and 31 such that the second mean: last mean=5:14; find n.       8

55) The perpendicular of a right angle triangle is 9cm and the three sides are in AP. Find the integral value of the length of the hypotenuse.      15cm

56) A farmer undertakes to pay off a debt of Rs2700 by monthly installments . He pays Rs200 as the first installment and increases oevery subsequent installment by Rs25 over the immediate previous installment. In how many installments he debt will be cleared up ?    9

57) A person pays Rs975 in monthly installments , each installment is less than the former by Rs5. The amount of first installment is Rs100. In what time will the entire amount be paid?    15 months


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