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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 431 · 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 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 41 (c) 462 (d) 441
  2. 2.What is the sum of the first 9 terms of the AP 4, 10, 16, …? (a) 504 (b) 279 (c) 52 (d) 252
  3. 3.What is the 19th term of the AP 7, 10, 13, 16, …? (a) 61 (b) 64 (c) 57 (d) 54
  4. 4.What is the 28th term of the AP 19, 21, 23, 25, …? (a) 56 (b) 73 (c) 75 (d) 54
  5. 5.What is the 21st term of the AP 7, 9, 11, 13, …? (a) 42 (b) 40 (c) 47 (d) 49
  6. 6.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 435 (c) 841 (d) 870
  7. 7.What is the missing term in the AP 14, 20, 26, ?, 38? (a) 32 (b) 33 (c) 38 (d) 31
  8. 8.What is the 11th term of the AP 11, 20, 29, 38, …? (a) 101 (b) 110 (c) 90 (d) 99
  9. 9.What is the missing term in the AP 3, ?, 13, 18, 23? (a) 9 (b) 7 (c) 8 (d) 13
  10. 10.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 378 (c) 812 (d) 406
  11. 11.Which term of the AP 14, 20, 26, 32, … is 188? (a) 31st (b) 30th (c) 32nd (d) 29th
  12. 12.Which term of the AP 19, 28, 37, 46, … is 361? (a) 38th (b) 39th (c) 41st (d) 40th
  13. 13.What is the missing term in the AP 3, 11, 19, ?, 35? (a) 27 (b) 26 (c) 35 (d) 28
  14. 14.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 184 (b) 92 (c) 104 (d) 22
  15. 15.What is the sum of all the whole numbers from 1 to 48? (a) 2352 (b) 1176 (c) 1152 (d) 1128
  16. 16.What is the 33rd term of the AP 13, 19, 25, 31, …? (a) 205 (b) 192 (c) 198 (d) 211
  17. 17.Which term of the AP 3, 9, 15, 21, … is 201? (a) 33rd (b) 36th (c) 35th (d) 34th
  18. 18.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 190 (b) 350 (c) 175 (d) 31
  19. 19.What is the sum of the first 11 terms of the AP 1, 6, 11, …? (a) 572 (b) 286 (c) 291 (d) 51
  20. 20.What is the 38th term of the AP 16, 22, 28, 34, …? (a) 222 (b) 238 (c) 244 (d) 228
  21. 21.Which term of the AP 5, 9, 13, 17, … is 61? (a) 16th (b) 14th (c) 15th (d) 17th
  22. 22.What is the missing term in the AP 12, ?, 26, 33, 40? (a) 19 (b) 26 (c) 20 (d) 18
  23. 23.What is the missing term in the AP 15, 20, 25, ?, 35? (a) 30 (b) 29 (c) 35 (d) 31
  24. 24.What is the missing term in the AP 11, ?, 15, 17, 19? (a) 15 (b) 12 (c) 13 (d) 14
  25. 25.What is the 22nd term of the AP 18, 22, 26, 30, …? (a) 102 (b) 84 (c) 106 (d) 88
  26. 26.What is the missing term in the AP 15, ?, 31, 39, 47? (a) 24 (b) 23 (c) 22 (d) 31
  27. 27.What is the 19th term of the AP 19, 28, 37, 46, …? (a) 171 (b) 181 (c) 162 (d) 190
  28. 28.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 121 (c) 66 (d) 21
  29. 29.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 25 (d) 30
  30. 30.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 144 (c) 23 (d) 156
  31. 31.What is the 13th term of the AP 12, 18, 24, 30, …? (a) 72 (b) 90 (c) 78 (d) 84
  32. 32.Which term of the AP 15, 18, 21, 24, … is 120? (a) 40th (b) 35th (c) 36th (d) 37th
  33. 33.What is the sum of all the whole numbers from 1 to 95? (a) 9120 (b) 4561 (c) 4560 (d) 4465
  34. 34.What is the sum of the first 7 terms of the AP 9, 14, 19, …? (a) 336 (b) 39 (c) 173 (d) 168
  35. 35.What is the sum of all the whole numbers from 1 to 10? (a) 50 (b) 55 (c) 45 (d) 110
  36. 36.What is the 38th term of the AP 10, 15, 20, 25, …? (a) 190 (b) 200 (c) 185 (d) 195
  37. 37.What is the sum of all the whole numbers from 1 to 16? (a) 136 (b) 120 (c) 128 (d) 272
  38. 38.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 126 (b) 64 (c) 63 (d) 11
  39. 39.What is the 36th term of the AP 4, 13, 22, 31, …? (a) 324 (b) 319 (c) 315 (d) 328
  40. 40.What is the sum of the first 8 terms of the AP 8, 14, 20, …? (a) 232 (b) 50 (c) 256 (d) 464

Answer key

  1. 441
  2. 252
  3. 61
  4. 73
  5. 47
  6. 841
  7. 32
  8. 101
  9. 8
  10. 406
  11. 30th
  12. 39th
  13. 27
  14. 92
  15. 1176
  16. 205
  17. 34th
  18. 175
  19. 286
  20. 238
  21. 15th
  22. 19
  23. 30
  24. 13
  25. 102
  26. 23
  27. 181
  28. 121
  29. 25
  30. 144
  31. 84
  32. 36th
  33. 4560
  34. 168
  35. 55
  36. 195
  37. 136
  38. 63
  39. 319
  40. 232

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