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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 831 · 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 30th term of the AP 13, 22, 31, 40, …? (a) 261 (b) 274 (c) 270 (d) 283
  2. 2.What is the sum of all the whole numbers from 1 to 51? (a) 2652 (b) 1327 (c) 1275 (d) 1326
  3. 3.What is the missing term in the AP 1, 3, ?, 7, 9? (a) 4 (b) 5 (c) 7 (d) 6
  4. 4.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 17 (b) 58 (c) 55 (d) 110
  5. 5.What is the sum of all the whole numbers from 1 to 36? (a) 666 (b) 630 (c) 1332 (d) 648
  6. 6.What is the 30th term of the AP 18, 24, 30, 36, …? (a) 174 (b) 198 (c) 180 (d) 192
  7. 7.Which term of the AP 3, 6, 9, 12, … is 60? (a) 22nd (b) 21st (c) 20th (d) 19th
  8. 8.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 506 (c) 253 (d) 43
  9. 9.What is the 26th term of the AP 11, 14, 17, 20, …? (a) 86 (b) 75 (c) 78 (d) 89
  10. 10.What is the missing term in the AP 3, 11, 19, ?, 35? (a) 35 (b) 26 (c) 28 (d) 27
  11. 11.What is the 14th term of the AP 14, 21, 28, 35, …? (a) 98 (b) 91 (c) 105 (d) 112
  12. 12.What is the 10th term of the AP 5, 9, 13, 17, …? (a) 36 (b) 40 (c) 41 (d) 45
  13. 13.What is the sum of all the whole numbers from 1 to 83? (a) 6972 (b) 3403 (c) 3486 (d) 3487
  14. 14.What is the sum of all the whole numbers from 1 to 35? (a) 595 (b) 1260 (c) 631 (d) 630
  15. 15.What is the sum of all the whole numbers from 1 to 10? (a) 50 (b) 45 (c) 55 (d) 110
  16. 16.Which term of the AP 16, 21, 26, 31, … is 131? (a) 23rd (b) 25th (c) 26th (d) 24th
  17. 17.What is the 28th term of the AP 13, 20, 27, 34, …? (a) 196 (b) 189 (c) 202 (d) 209
  18. 18.What is the sum of all the whole numbers from 1 to 40? (a) 800 (b) 1640 (c) 780 (d) 820
  19. 19.What is the 23rd term of the AP 11, 15, 19, 23, …? (a) 103 (b) 92 (c) 88 (d) 99
  20. 20.What is the sum of the first 7 terms of the AP 10, 14, 18, …? (a) 168 (b) 34 (c) 308 (d) 154
  21. 21.What is the 37th term of the AP 6, 13, 20, 27, …? (a) 258 (b) 265 (c) 252 (d) 259
  22. 22.What is the sum of all the whole numbers from 1 to 93? (a) 4371 (b) 8742 (c) 4278 (d) 4372
  23. 23.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 435 (c) 406 (d) 436
  24. 24.Which term of the AP 15, 20, 25, 30, … is 90? (a) 15th (b) 16th (c) 17th (d) 18th
  25. 25.What is the sum of the first 10 terms of the AP 7, 11, 15, …? (a) 500 (b) 250 (c) 270 (d) 43
  26. 26.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 171 (b) 306 (c) 153 (d) 33
  27. 27.What is the missing term in the AP 1, 6, ?, 16, 21? (a) 12 (b) 10 (c) 16 (d) 11
  28. 28.What is the sum of all the whole numbers from 1 to 23? (a) 552 (b) 277 (c) 253 (d) 276
  29. 29.What is the 33rd term of the AP 9, 17, 25, 33, …? (a) 256 (b) 264 (c) 265 (d) 273
  30. 30.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 50 (b) 90 (c) 13 (d) 45
  31. 31.What is the sum of the first 12 terms of the AP 6, 12, 18, …? (a) 72 (b) 936 (c) 468 (d) 504
  32. 32.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 30 (b) 165 (c) 324 (d) 162
  33. 33.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 66 (c) 21 (d) 121
  34. 34.Which term of the AP 8, 15, 22, 29, … is 99? (a) 16th (b) 14th (c) 15th (d) 13th
  35. 35.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 841 (c) 870 (d) 57
  36. 36.What is the sum of the first 8 terms of the AP 9, 13, 17, …? (a) 37 (b) 200 (c) 368 (d) 184
  37. 37.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 19 (c) 100 (d) 55
  38. 38.What is the missing term in the AP 5, ?, 23, 32, 41? (a) 14 (b) 23 (c) 13 (d) 15
  39. 39.Which term of the AP 15, 22, 29, 36, … is 281? (a) 40th (b) 39th (c) 41st (d) 38th
  40. 40.What is the missing term in the AP 11, ?, 23, 29, 35? (a) 18 (b) 16 (c) 23 (d) 17

Answer key

  1. 274
  2. 1326
  3. 5
  4. 55
  5. 666
  6. 192
  7. 20th
  8. 484
  9. 86
  10. 27
  11. 105
  12. 41
  13. 3486
  14. 630
  15. 55
  16. 24th
  17. 202
  18. 820
  19. 99
  20. 154
  21. 258
  22. 4371
  23. 435
  24. 16th
  25. 250
  26. 153
  27. 11
  28. 276
  29. 265
  30. 45
  31. 468
  32. 162
  33. 121
  34. 14th
  35. 841
  36. 184
  37. 100
  38. 14
  39. 39th
  40. 17

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