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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 82 · 40 questions
TalentJR

How to solve it (Same step every time): In an AP the gap (common difference d) is always the same. nth term = a + (n − 1) × d, where a is the first term. Sum of n terms = n × (first + last) ÷ 2; so 1 + 2 + … + n = n × (n + 1) ÷ 2, and the first n odd numbers add up to n × n.

NameDateTime takenScore ___ / 40
  1. 1.What is the 32nd term of the AP 20, 29, 38, 47, …? (a) 288 (b) 279 (c) 299 (d) 308
  2. 2.What is the 17th term of the AP 1, 5, 9, 13, …? (a) 65 (b) 68 (c) 69 (d) 64
  3. 3.What is the sum of the first 9 terms of the AP 8, 14, 20, …? (a) 288 (b) 56 (c) 315 (d) 576
  4. 4.What is the 14th term of the AP 16, 23, 30, 37, …? (a) 98 (b) 107 (c) 114 (d) 91
  5. 5.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 47 (c) 300 (d) 576
  6. 6.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 11 (c) 36 (d) 21
  7. 7.What is the 32nd term of the AP 4, 12, 20, 28, …? (a) 260 (b) 252 (c) 256 (d) 248
  8. 8.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 828 (b) 414 (c) 62 (d) 444
  9. 9.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 63 (b) 126 (c) 66 (d) 13
  10. 10.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 144 (b) 12 (c) 73 (d) 72
  11. 11.What is the missing term in the AP 6, 15, 24, ?, 42? (a) 34 (b) 42 (c) 32 (d) 33
  12. 12.What is the missing term in the AP 8, 14, 20, ?, 32? (a) 25 (b) 32 (c) 26 (d) 27
  13. 13.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 24 (b) 210 (c) 108 (d) 105
  14. 14.What is the sum of all the whole numbers from 1 to 33? (a) 1122 (b) 528 (c) 562 (d) 561
  15. 15.What is the 17th term of the AP 20, 29, 38, 47, …? (a) 173 (b) 164 (c) 144 (d) 153
  16. 16.What is the missing term in the AP 7, 10, ?, 16, 19? (a) 12 (b) 14 (c) 16 (d) 13
  17. 17.What is the 30th term of the AP 3, 10, 17, 24, …? (a) 213 (b) 210 (c) 203 (d) 206
  18. 18.What is the 26th term of the AP 4, 9, 14, 19, …? (a) 125 (b) 130 (c) 129 (d) 134
  19. 19.What is the sum of all the whole numbers from 1 to 16? (a) 120 (b) 136 (c) 272 (d) 128
  20. 20.What is the 12th term of the AP 20, 24, 28, 32, …? (a) 44 (b) 64 (c) 48 (d) 68
  21. 21.What is the missing term in the AP 12, ?, 16, 18, 20? (a) 14 (b) 15 (c) 16 (d) 13
  22. 22.What is the 13th term of the AP 17, 19, 21, 23, …? (a) 26 (b) 41 (c) 24 (d) 43
  23. 23.What is the sum of the first 10 terms of the AP 1, 7, 13, …? (a) 55 (b) 280 (c) 560 (d) 310
  24. 24.Which term of the AP 8, 17, 26, 35, … is 89? (a) 12th (b) 9th (c) 10th (d) 11th
  25. 25.What is the sum of all the whole numbers from 1 to 72? (a) 2556 (b) 2628 (c) 2592 (d) 5256
  26. 26.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 66 (c) 121 (d) 132
  27. 27.What is the 20th term of the AP 18, 23, 28, 33, …? (a) 118 (b) 100 (c) 95 (d) 113
  28. 28.What is the sum of all the whole numbers from 1 to 53? (a) 2862 (b) 1431 (c) 1378 (d) 1432
  29. 29.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 120 (b) 220 (c) 110 (d) 20
  30. 30.What is the 16th term of the AP 12, 14, 16, 18, …? (a) 30 (b) 32 (c) 42 (d) 44
  31. 31.What is the 10th term of the AP 1, 6, 11, 16, …? (a) 46 (b) 51 (c) 45 (d) 50
  32. 32.What is the missing term in the AP 15, 18, ?, 24, 27? (a) 20 (b) 24 (c) 21 (d) 22
  33. 33.What is the 10th term of the AP 6, 9, 12, 15, …? (a) 30 (b) 36 (c) 33 (d) 27
  34. 34.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 56 (c) 13 (d) 49
  35. 35.Which term of the AP 3, 12, 21, 30, … is 75? (a) 8th (b) 10th (c) 9th (d) 11th
  36. 36.What is the 30th term of the AP 5, 9, 13, 17, …? (a) 121 (b) 120 (c) 116 (d) 125
  37. 37.What is the 27th term of the AP 14, 18, 22, 26, …? (a) 104 (b) 108 (c) 122 (d) 118
  38. 38.What is the sum of the first 7 terms of the AP 9, 15, 21, …? (a) 189 (b) 45 (c) 210 (d) 378
  39. 39.What is the sum of the first 10 terms of the AP 8, 9, 10, …? (a) 250 (b) 17 (c) 125 (d) 130
  40. 40.What is the sum of the first 12 terms of the AP 4, 9, 14, …? (a) 408 (b) 378 (c) 59 (d) 756

Answer key

  1. 299
  2. 65
  3. 288
  4. 107
  5. 576
  6. 36
  7. 252
  8. 414
  9. 63
  10. 72
  11. 33
  12. 26
  13. 105
  14. 561
  15. 164
  16. 13
  17. 206
  18. 129
  19. 136
  20. 64
  21. 14
  22. 41
  23. 280
  24. 10th
  25. 2628
  26. 121
  27. 113
  28. 1431
  29. 110
  30. 42
  31. 46
  32. 21
  33. 33
  34. 49
  35. 9th
  36. 121
  37. 118
  38. 189
  39. 125
  40. 378

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