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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 976 · 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 sum of the first 11 terms of the AP 10, 14, 18, …? (a) 50 (b) 352 (c) 660 (d) 330
  2. 2.What is the 28th term of the AP 11, 16, 21, 26, …? (a) 146 (b) 135 (c) 140 (d) 151
  3. 3.What is the 35th term of the AP 5, 12, 19, 26, …? (a) 238 (b) 243 (c) 245 (d) 250
  4. 4.What is the sum of all the whole numbers from 1 to 85? (a) 3655 (b) 3656 (c) 3570 (d) 7310
  5. 5.What is the missing term in the AP 15, 17, 19, ?, 23? (a) 23 (b) 20 (c) 22 (d) 21
  6. 6.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 182 (b) 22 (c) 91 (d) 94
  7. 7.Which term of the AP 10, 17, 24, 31, … is 283? (a) 39th (b) 41st (c) 40th (d) 42nd
  8. 8.Which term of the AP 20, 23, 26, 29, … is 71? (a) 17th (b) 19th (c) 20th (d) 18th
  9. 9.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 29 (c) 120 (d) 240
  10. 10.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 576 (d) 600
  11. 11.What is the 30th term of the AP 12, 19, 26, 33, …? (a) 203 (b) 210 (c) 215 (d) 222
  12. 12.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 17 (b) 78 (c) 144 (d) 72
  13. 13.What is the missing term in the AP 17, 22, 27, ?, 37? (a) 32 (b) 37 (c) 31 (d) 33
  14. 14.What is the sum of the first 7 terms of the AP 7, 8, 9, …? (a) 71 (b) 140 (c) 13 (d) 70
  15. 15.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 13 (c) 56 (d) 28
  16. 16.What is the sum of all the whole numbers from 1 to 93? (a) 4372 (b) 8742 (c) 4371 (d) 4278
  17. 17.What is the 39th term of the AP 12, 15, 18, 21, …? (a) 126 (b) 117 (c) 129 (d) 114
  18. 18.What is the 15th term of the AP 5, 7, 9, 11, …? (a) 30 (b) 35 (c) 33 (d) 28
  19. 19.What is the sum of the first 9 terms of the AP 4, 7, 10, …? (a) 288 (b) 28 (c) 147 (d) 144
  20. 20.What is the sum of the first 12 terms of the AP 3, 6, 9, …? (a) 36 (b) 468 (c) 252 (d) 234
  21. 21.What is the 32nd term of the AP 7, 13, 19, 25, …? (a) 186 (b) 192 (c) 199 (d) 193
  22. 22.What is the 30th term of the AP 18, 26, 34, 42, …? (a) 232 (b) 250 (c) 258 (d) 240
  23. 23.What is the 35th term of the AP 16, 22, 28, 34, …? (a) 220 (b) 210 (c) 226 (d) 204
  24. 24.What is the missing term in the AP 4, ?, 20, 28, 36? (a) 20 (b) 13 (c) 11 (d) 12
  25. 25.What is the sum of the first 8 terms of the AP 8, 12, 16, …? (a) 176 (b) 36 (c) 192 (d) 352
  26. 26.What is the missing term in the AP 4, ?, 10, 13, 16? (a) 7 (b) 10 (c) 6 (d) 8
  27. 27.What is the 33rd term of the AP 14, 21, 28, 35, …? (a) 238 (b) 231 (c) 245 (d) 224
  28. 28.What is the sum of the first 10 terms of the AP 5, 9, 13, …? (a) 250 (b) 41 (c) 230 (d) 460
  29. 29.What is the sum of the first 10 terms of the AP 8, 9, 10, …? (a) 130 (b) 250 (c) 125 (d) 17
  30. 30.What is the 38th term of the AP 17, 19, 21, 23, …? (a) 76 (b) 74 (c) 91 (d) 93
  31. 31.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 110 (b) 65 (c) 19 (d) 55
  32. 32.What is the sum of all the whole numbers from 1 to 71? (a) 5112 (b) 2556 (c) 2485 (d) 2557
  33. 33.What is the 28th term of the AP 14, 21, 28, 35, …? (a) 210 (b) 189 (c) 196 (d) 203
  34. 34.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 96 (b) 88 (c) 176 (d) 18
  35. 35.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 45 (c) 90 (d) 81
  36. 36.What is the 35th term of the AP 19, 26, 33, 40, …? (a) 238 (b) 257 (c) 245 (d) 264
  37. 37.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 240 (b) 31 (c) 480 (d) 252
  38. 38.What is the sum of all the whole numbers from 1 to 54? (a) 1431 (b) 1458 (c) 2970 (d) 1485
  39. 39.What is the sum of all the whole numbers from 1 to 50? (a) 1225 (b) 1250 (c) 2550 (d) 1275
  40. 40.What is the sum of all the whole numbers from 1 to 28? (a) 406 (b) 378 (c) 812 (d) 392

Answer key

  1. 330
  2. 146
  3. 243
  4. 3655
  5. 21
  6. 91
  7. 40th
  8. 18th
  9. 225
  10. 576
  11. 215
  12. 72
  13. 32
  14. 70
  15. 49
  16. 4371
  17. 126
  18. 33
  19. 144
  20. 234
  21. 193
  22. 250
  23. 220
  24. 12
  25. 176
  26. 7
  27. 238
  28. 230
  29. 125
  30. 91
  31. 55
  32. 2556
  33. 203
  34. 88
  35. 81
  36. 257
  37. 240
  38. 1485
  39. 1275
  40. 406

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