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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 89 · 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 34th term of the AP 8, 11, 14, 17, …? (a) 110 (b) 99 (c) 102 (d) 107
  2. 2.What is the 20th term of the AP 9, 18, 27, 36, …? (a) 180 (b) 189 (c) 181 (d) 171
  3. 3.What is the sum of the first 10 terms of the AP 3, 6, 9, …? (a) 165 (b) 30 (c) 180 (d) 330
  4. 4.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 21 (c) 132 (d) 121
  5. 5.What is the sum of all the whole numbers from 1 to 68? (a) 2312 (b) 2278 (c) 4692 (d) 2346
  6. 6.What is the sum of the first 7 terms of the AP 9, 11, 13, …? (a) 21 (b) 105 (c) 112 (d) 210
  7. 7.What is the sum of the first 12 terms of the AP 2, 4, 6, …? (a) 168 (b) 24 (c) 156 (d) 312
  8. 8.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 10 (b) 9 (c) 8 (d) 12
  9. 9.What is the 17th term of the AP 8, 12, 16, 20, …? (a) 72 (b) 64 (c) 76 (d) 68
  10. 10.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 252 (b) 240 (c) 31 (d) 480
  11. 11.What is the 16th term of the AP 3, 11, 19, 27, …? (a) 123 (b) 131 (c) 120 (d) 128
  12. 12.What is the missing term in the AP 11, 19, 27, ?, 43? (a) 34 (b) 35 (c) 43 (d) 36
  13. 13.What is the 10th term of the AP 7, 11, 15, 19, …? (a) 36 (b) 47 (c) 40 (d) 43
  14. 14.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 144 (d) 156
  15. 15.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 6 (b) 20 (c) 21 (d) 40
  16. 16.What is the 13th term of the AP 8, 13, 18, 23, …? (a) 73 (b) 60 (c) 65 (d) 68
  17. 17.What is the 29th term of the AP 19, 27, 35, 43, …? (a) 224 (b) 232 (c) 243 (d) 251
  18. 18.What is the 19th term of the AP 1, 7, 13, 19, …? (a) 114 (b) 108 (c) 115 (d) 109
  19. 19.What is the 33rd term of the AP 4, 12, 20, 28, …? (a) 256 (b) 264 (c) 260 (d) 268
  20. 20.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 210 (b) 34 (c) 228 (d) 420
  21. 21.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 30 (b) 210 (c) 105 (d) 120
  22. 22.What is the 13th term of the AP 9, 14, 19, 24, …? (a) 69 (b) 74 (c) 65 (d) 60
  23. 23.What is the 12th term of the AP 1, 8, 15, 22, …? (a) 85 (b) 78 (c) 77 (d) 84
  24. 24.What is the missing term in the AP 12, 19, ?, 33, 40? (a) 27 (b) 26 (c) 33 (d) 25
  25. 25.What is the missing term in the AP 14, 19, ?, 29, 34? (a) 25 (b) 23 (c) 29 (d) 24
  26. 26.What is the sum of all the whole numbers from 1 to 52? (a) 1352 (b) 1378 (c) 1326 (d) 2756
  27. 27.What is the 20th term of the AP 9, 13, 17, 21, …? (a) 80 (b) 85 (c) 76 (d) 89
  28. 28.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 1122 (c) 562 (d) 528
  29. 29.What is the sum of the first 9 terms of the AP 10, 14, 18, …? (a) 234 (b) 42 (c) 468 (d) 252
  30. 30.What is the 21st term of the AP 13, 22, 31, 40, …? (a) 193 (b) 180 (c) 202 (d) 189
  31. 31.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 324 (b) 171 (c) 26 (d) 162
  32. 32.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 169 (c) 182 (d) 91
  33. 33.What is the sum of the first 11 terms of the AP 8, 10, 12, …? (a) 396 (b) 209 (c) 198 (d) 28
  34. 34.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 143 (b) 18 (c) 144 (d) 286
  35. 35.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 127 (b) 252 (c) 18 (d) 126
  36. 36.What is the sum of the first 8 terms of the AP 9, 13, 17, …? (a) 368 (b) 37 (c) 200 (d) 184
  37. 37.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 324 (c) 342 (d) 171
  38. 38.What is the sum of the first 12 terms of the AP 9, 14, 19, …? (a) 876 (b) 64 (c) 468 (d) 438
  39. 39.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 15 (b) 99 (c) 100 (d) 198
  40. 40.What is the missing term in the AP 20, ?, 26, 29, 32? (a) 23 (b) 22 (c) 26 (d) 24

Answer key

  1. 107
  2. 180
  3. 165
  4. 121
  5. 2346
  6. 105
  7. 156
  8. 9
  9. 72
  10. 240
  11. 123
  12. 35
  13. 43
  14. 144
  15. 20
  16. 68
  17. 243
  18. 109
  19. 260
  20. 210
  21. 105
  22. 69
  23. 78
  24. 26
  25. 24
  26. 1378
  27. 85
  28. 561
  29. 234
  30. 193
  31. 162
  32. 169
  33. 198
  34. 143
  35. 126
  36. 184
  37. 324
  38. 438
  39. 99
  40. 23

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