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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 738 · 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 all the whole numbers from 1 to 94? (a) 8930 (b) 4371 (c) 4418 (d) 4465
  2. 2.What is the sum of all the whole numbers from 1 to 89? (a) 3916 (b) 4005 (c) 4006 (d) 8010
  3. 3.What is the 13th term of the AP 4, 8, 12, 16, …? (a) 53 (b) 52 (c) 48 (d) 56
  4. 4.Which term of the AP 2, 9, 16, 23, … is 114? (a) 16th (b) 18th (c) 17th (d) 19th
  5. 5.What is the 33rd term of the AP 4, 9, 14, 19, …? (a) 165 (b) 160 (c) 164 (d) 169
  6. 6.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 34 (b) 114 (c) 228 (d) 132
  7. 7.What is the 30th term of the AP 3, 11, 19, 27, …? (a) 240 (b) 235 (c) 243 (d) 232
  8. 8.What is the sum of the first 10 terms of the AP 4, 10, 16, …? (a) 620 (b) 58 (c) 310 (d) 340
  9. 9.What is the 26th term of the AP 3, 5, 7, 9, …? (a) 55 (b) 53 (c) 52 (d) 50
  10. 10.What is the 31st term of the AP 16, 25, 34, 43, …? (a) 270 (b) 279 (c) 295 (d) 286
  11. 11.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 39 (b) 144 (c) 288 (d) 162
  12. 12.What is the missing term in the AP 5, ?, 19, 26, 33? (a) 11 (b) 12 (c) 19 (d) 13
  13. 13.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 28 (b) 93 (c) 108 (d) 186
  14. 14.Which term of the AP 15, 20, 25, 30, … is 105? (a) 20th (b) 21st (c) 18th (d) 19th
  15. 15.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 65 (b) 130 (c) 70 (d) 11
  16. 16.What is the missing term in the AP 7, 12, ?, 22, 27? (a) 17 (b) 16 (c) 18 (d) 22
  17. 17.What is the sum of all the whole numbers from 1 to 28? (a) 406 (b) 378 (c) 812 (d) 392
  18. 18.What is the 37th term of the AP 7, 12, 17, 22, …? (a) 187 (b) 192 (c) 185 (d) 180
  19. 19.Which term of the AP 20, 22, 24, 26, … is 50? (a) 15th (b) 25th (c) 17th (d) 16th
  20. 20.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 120 (c) 225 (d) 240
  21. 21.What is the missing term in the AP 17, ?, 25, 29, 33? (a) 22 (b) 21 (c) 25 (d) 20
  22. 22.What is the missing term in the AP 6, 10, 14, ?, 22? (a) 19 (b) 17 (c) 22 (d) 18
  23. 23.What is the missing term in the AP 2, ?, 20, 29, 38? (a) 11 (b) 20 (c) 10 (d) 12
  24. 24.Which term of the AP 14, 16, 18, 20, … is 88? (a) 44th (b) 37th (c) 39th (d) 38th
  25. 25.What is the sum of the first 9 terms of the AP 1, 7, 13, …? (a) 225 (b) 49 (c) 252 (d) 450
  26. 26.Which term of the AP 13, 15, 17, 19, … is 67? (a) 27th (b) 30th (c) 29th (d) 28th
  27. 27.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 324 (c) 342 (d) 35
  28. 28.What is the missing term in the AP 9, ?, 15, 18, 21? (a) 15 (b) 11 (c) 13 (d) 12
  29. 29.What is the sum of the first 11 terms of the AP 7, 10, 13, …? (a) 242 (b) 484 (c) 37 (d) 245
  30. 30.Which term of the AP 20, 27, 34, 41, … is 125? (a) 17th (b) 16th (c) 15th (d) 18th
  31. 31.What is the 17th term of the AP 20, 22, 24, 26, …? (a) 32 (b) 52 (c) 34 (d) 54
  32. 32.What is the 15th term of the AP 8, 10, 12, 14, …? (a) 28 (b) 38 (c) 30 (d) 36
  33. 33.What is the sum of all the whole numbers from 1 to 51? (a) 1326 (b) 1275 (c) 2652 (d) 1327
  34. 34.What is the 36th term of the AP 2, 4, 6, 8, …? (a) 74 (b) 70 (c) 73 (d) 72
  35. 35.What is the sum of all the whole numbers from 1 to 71? (a) 5112 (b) 2556 (c) 2557 (d) 2485
  36. 36.Which term of the AP 13, 21, 29, 37, … is 285? (a) 34th (b) 36th (c) 35th (d) 37th
  37. 37.Which term of the AP 2, 10, 18, 26, … is 282? (a) 37th (b) 38th (c) 36th (d) 35th
  38. 38.What is the missing term in the AP 16, ?, 24, 28, 32? (a) 19 (b) 21 (c) 20 (d) 24
  39. 39.What is the 15th term of the AP 9, 13, 17, 21, …? (a) 60 (b) 65 (c) 69 (d) 56
  40. 40.What is the 27th term of the AP 19, 26, 33, 40, …? (a) 189 (b) 201 (c) 182 (d) 208

Answer key

  1. 4465
  2. 4005
  3. 52
  4. 17th
  5. 164
  6. 114
  7. 235
  8. 310
  9. 53
  10. 286
  11. 144
  12. 12
  13. 93
  14. 19th
  15. 65
  16. 17
  17. 406
  18. 187
  19. 16th
  20. 225
  21. 21
  22. 18
  23. 11
  24. 38th
  25. 225
  26. 28th
  27. 324
  28. 12
  29. 242
  30. 16th
  31. 52
  32. 36
  33. 1326
  34. 72
  35. 2556
  36. 35th
  37. 36th
  38. 20
  39. 65
  40. 201

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