AIRTHEMATIC PROGRESSION
I. Multiple Choice Questions
Each of the following questions has 4 alternatives, out of which only one is correct. Point out the correct alternative.
1. The common difference of the AP -2, -3, -4, .....is
(a) .3 (b) .1 (c) .1 (d) -.2
2. If the first term of an AP is 2.5 and the common difference is .3, then
the 15th term of the AP is
(a) 7.6 (b) 6.7 (c) 5.7 (d) 5.6
3. If the 5th term of an AP is 12 and 8th term of the AP is 16, then it
common difference is
(a) 3 (b) 4 / 3 (c) 2 / 3 (d) 3 / 4
4. In an AP, if common difference d = 3, then t7 -t9 is equal to
(a) 2 (b) -2 (c) 6 (d) -6
5. The 15th term from the end in the AP 13,16,19,…..,160 is
(a) 128 (b) 118 (c) 98 (d) 108
6. The 12th term from the end in the AP 9,5,1,…..is -107. Then the last
term is
(a) -151 (b) -155 (c) -147 (d) -159
7. The 10th term from the end in the AP 5,8,11,….. is 95 then the number
of terms in the AP are
(a) 38 (b) 40 (c) 42 (d) 43
8. If the last term of an AP is 119 and the 8th term from the end is 91 then the common difference of the AP is
(a) 2 (b) 4 (c) 3 (d) -3
9. In an AP, if d = -4, n = 7, a = 4, then a =
(a) 6 (b) 7 (c) 20 (d) 28
10. In an AP, if a = 3.5, d = 0 and n = 101, then a =
(a) 0 (b) 3.5 (c) 103.5 (d) 104.5
11. The common difference of the AP whose general term a = 2n + 1 is
(a) 1 (b) 2 (c) -2 (d) -1
12. The number of terms in the AP 2, 5, 8, ....., 59 is
(a) 12 (b) 19 (c) 20 (d) 25
13. The first positive term of the AP -11, -8, -5, ..... is
(a) 5th term (b) 4th term
(c) 3rd term (d) 6th term
14. 4th term from the end in the AP 2, 5, 8, ....., 35 is
(a) 29 (b) 23 (c) 20 (d) 26
15. Which of the following is not an AP ?
(a) 1, 4, 7, 10, ..... (b) -5, -2, 1, 4, .....
(c) 3, 7, 12, 18, ..... (d) 11, 14, 17, 20, .....
16. The 21st term of the AP, whose first two terms are -3 and 4, is
(a) 17 (b) 137 (c) 143 (d) -143
17. In an AP t₁,t₂,....,tn , if t₁=5, t₂ = 8, t = 113 then n=
(a) 37 (b) 38 (c) 39 (d) 36
18. In an AP t₁,t₂,....,tn , if t₁ = 13, t₂ = 17 then t₁7 =
(a) 97 (b) 87 (c) 77 (d) 69
19. If the 17th term of an AP exceeds the 13th term of the AP by 15, then
the common difference is
(a) 3 (b) 3.75 (c) 3.5 (d) 4.25
20. If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th
term ?
(a) 33 (b) 30 (c) 37 (d) 38
21. The next term of the AP √8, √18,√32, ..... is
(a) 5√2 (b) 5√3 (c) 3√3 (d) 4√3
22. The 11th and 13th terms of an AP are respectively 35 and 41. The
common difference of the AP is
(a) 38 (b) 2 (c) 6 (d) 3
23. The sum of first 20 odd natural numbers is
(a) 281 (b) 285 (c) 400 (d) 421
24. If for an AP a₅ = a₁₀ = 71, then a₁₅ is
(a) 72 (b) 71 (c) 76 (d) 66
25. The sum of first 20 natural numbers is
(a) 110 (b) 170 (c) 190 (d) 210
26. If the common difference of an AP is 5, then a₁₈ - a₁₃ =
(a) 5 (b) 20 (c) 30 (d) 25
27. What is the common difference of an AP in which a₁₈ - a₁₄ = 32 ?
(a) 8 (b) -8 (c) -4 (d) 4
28. If {an} = {2.5, 2.51, 2.52, .....} and {bn} = {3.72, 3.73, 3.74, .....} be two
AP's then a₁₀₀₀₀₅ - b₁₀₀₀₀₅ =
(a) -1.22 (b) 1.22 (c) 1.2 (d) -1.02
29. The value of a₃₀ - a₂₀ for the AP - 9, -14, -19, ..... is
(a) -35 (b) -50 (c) -55 (d) -65
30. If a be the kth term of the AP 3, 15, 27, 39, ..... and value of a, is 180
more than the value of as then k
(a) 58 (b) 62 (c) 65 (d) 68
31. 7 times the 7th term of an AP is equal to 11 times the 11th term, then
its 18th term is equal to
(a) 7 (b) 11 (c) 18 (d) 0
32. Two s have the same common difference. The first term of one is - 1 and that of the second is - 8, then the difference between their 4th terms is
(a)-1 (b)-8 (c) 7 (d)-9
33. The sum of first 16 terms of the AP 10, 6, 2, .... is
(a)-320 (b) 320 (c)-352 (d)-400
34. The sum of the first 11 terms of the AP 2, 6, 10, .....is
(a) 238 (b) 242 (c) 246 (d) 254
35. The sum (-6)+(0) + (6) +.....to 13 terms is equal to
(a) 390 (b) 384 (c) 378 (d) 396
36. The sum of 2+5+8+.....+ 152 is
(a) 3924 (b) 3927 (c) 3936 (d) 3942
37. In an AP, if a = 1, a = 20 and S, 399, then n =
(a) 19 (b) 21 (c) 38 (d) 42
38. The 4th term from the end of the AP-11,-8,-5, 49 is
(a) 37 (b) 40 (c) 43 (d) 58
39. If the first term of an AP is -5 and the common difference is 2, then
the sum of first 6 terms is
(a) 0 (b) 5 (c) 6 (d) 15
40. If sum to n terms of an AP is 3 n² + 4 n, then the common difference
of the AP is
(a) 3 (b) 4 (c) 6 (d) 7
41. If the sum of the AP 3, 7, 11,..... is 210, then the number of terms in
this AP is
(a) 12 (b) 15 (c) 10 (d) 11
42. The sum of first 10 multiples of 7 is
(a) 385 (b) 315 (c) 371 (d) 406
43. If the nth term of a sequence is 5 + 2 n, then the sum to first 20 terms
is
(a) 485 (b) 520 (c) 525 (d) 540
44. If pth term of the sequence 21, 42, 63, ... is 420, then p =
(a) 20 (b) 21 (c) 22 (d) 19
45. The famous mathematician associated with finding the sum of the
first 100 natural numbers is
(a) Pythagoras (b) Newton
(c) Euclid (d) Gauss
46. If Sn denotes the sum of first n terms of an AP, then Sn - 2Sn-1 + Sn-2
(n ≥ 3) is equal to
(a) Tn (b) Tn-1 (c) C.D. (d) None of these
(HINT. Sn - 2Sn-1 + Sn-2 = (Sn - Sn-1) - (Sn-1 - Sn-2) = Tn - Tn-1)
47. The 10th term of the AP 5, 8, 11, 14, ..... is
(a) 32 (b) 35 (c) 38 (d) 185
48. The sum of first five multiples of 3 is
(a) 65 (b) 75 (c) 45 (d) 55
49. In an AP if a = -7.2, d = 3.6, an = 7.2, then n is
(a) 1 (b) 3 (c) 4 (d) 5
50. 11th term of the AP -5, -5, 0, 5, ..... is
(a) -20 (b) 20 (c) -30 (d) 30
II. Fill in the Blanks
1. The sequence 1, 1/2, 1/3, 1/4, 1/5 is ________ an AP.
2. If a1 + a24 = 100 in an AP, then a2 + a23 = ________
3. Squares of natural numbers taken in order ________ from an AP
4. The next term of the sequence √3, √12, √27, √48 is ________
5. The nth term of an AP ________ be n² - 1.
6. ________ term of the AP 12, 10, 8, ________is 0.
7. Common difference of the AP -1, -1, -1, -1, -1, ________is
8. 6th term of the sequence 3, 33, 333, ________ is
9. ________ term of the AP - 13, -9, -5, ________is the first positive term.
10. If the nth term of an AP is 2 - 3/4 n, then its common difference is
III. True/False Statements
In case of each of the following statements, state whether it is true or false:
1. For the AP 10, 5, 0, -5, ......the common difference is equal to 5.
2. The sequence 1, 2, 1, 2, 1, 2, ......is an AP.
3. The sequence 0.1, 0.1, 0.1, ......is an AP.
4. If the nth term of a sequence is a linear polynomial in 'n', then it is an AP.
5. '0' is one of the terms of the AP 33, 29, 25, 21, ......?
6. If the nth term of a sequence is n² - n + 1, then it cannot be an AP.
7. If the sum of first n terms of an AP is n², then its common difference is 2.
8. The sequence 1³, 2³, 3³, ...... is an AP.
9. The sequence 1/2, 2/2², 3/2³, ...... is an AP.
10. For the AP a, a+d, a+2 d, ......lm - ln = (m-n) d.
11. The nth term of an AP cannot be n² + 1.
12. 0 is a term of the AP 31, 28, 25, ......
13. The sequence 1², 2², 3², ...... is an AP.
14. The sequence 11, 22, 33, ...... is an AP.
15. The sequence √3, √12, √27, √48, ......is not an AP
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