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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 256 · 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 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 324 (c) 171 (d) 342
  2. 2.What is the missing term in the AP 3, 8, ?, 18, 23? (a) 12 (b) 13 (c) 14 (d) 18
  3. 3.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 17 (b) 90 (c) 45 (d) 55
  4. 4.What is the 15th term of the AP 7, 10, 13, 16, …? (a) 45 (b) 52 (c) 42 (d) 49
  5. 5.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 30 (b) 228 (c) 240 (d) 456
  6. 6.What is the sum of the first 7 terms of the AP 5, 10, 15, …? (a) 35 (b) 145 (c) 140 (d) 280
  7. 7.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 28 (c) 13 (d) 56
  8. 8.What is the 31st term of the AP 8, 17, 26, 35, …? (a) 279 (b) 278 (c) 270 (d) 287
  9. 9.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 39 (c) 400 (d) 420
  10. 10.What is the sum of the first 11 terms of the AP 8, 14, 20, …? (a) 836 (b) 68 (c) 418 (d) 451
  11. 11.Which term of the AP 2, 7, 12, 17, … is 97? (a) 19th (b) 22nd (c) 20th (d) 21st
  12. 12.What is the sum of the first 12 terms of the AP 8, 14, 20, …? (a) 492 (b) 528 (c) 984 (d) 74
  13. 13.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 156 (b) 288 (c) 144 (d) 23
  14. 14.What is the sum of the first 7 terms of the AP 8, 10, 12, …? (a) 105 (b) 196 (c) 20 (d) 98
  15. 15.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 414 (b) 62 (c) 828 (d) 444
  16. 16.Which term of the AP 7, 16, 25, 34, … is 106? (a) 13th (b) 12th (c) 14th (d) 11th
  17. 17.What is the 40th term of the AP 13, 15, 17, 19, …? (a) 93 (b) 80 (c) 91 (d) 78
  18. 18.What is the sum of all the whole numbers from 1 to 81? (a) 6642 (b) 3321 (c) 3322 (d) 3240
  19. 19.Which term of the AP 14, 16, 18, 20, … is 38? (a) 19th (b) 12th (c) 14th (d) 13th
  20. 20.What is the 38th term of the AP 4, 12, 20, 28, …? (a) 296 (b) 300 (c) 304 (d) 308
  21. 21.What is the 35th term of the AP 2, 11, 20, 29, …? (a) 317 (b) 315 (c) 306 (d) 308
  22. 22.Which term of the AP 12, 21, 30, 39, … is 93? (a) 9th (b) 11th (c) 12th (d) 10th
  23. 23.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 396 (b) 726 (c) 363 (d) 63
  24. 24.What is the 33rd term of the AP 1, 8, 15, 22, …? (a) 225 (b) 232 (c) 224 (d) 231
  25. 25.What is the 18th term of the AP 20, 23, 26, 29, …? (a) 51 (b) 54 (c) 74 (d) 71
  26. 26.What is the sum of all the whole numbers from 1 to 14? (a) 98 (b) 105 (c) 91 (d) 210
  27. 27.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 9 (c) 15 (d) 25
  28. 28.What is the 30th term of the AP 19, 23, 27, 31, …? (a) 139 (b) 135 (c) 116 (d) 120
  29. 29.What is the 23rd term of the AP 3, 12, 21, 30, …? (a) 201 (b) 210 (c) 207 (d) 198
  30. 30.What is the 40th term of the AP 5, 8, 11, 14, …? (a) 117 (b) 120 (c) 122 (d) 125
  31. 31.Which term of the AP 5, 10, 15, 20, … is 60? (a) 14th (b) 13th (c) 12th (d) 11th
  32. 32.What is the sum of all the whole numbers from 1 to 15? (a) 120 (b) 121 (c) 240 (d) 105
  33. 33.What is the missing term in the AP 16, 19, ?, 25, 28? (a) 25 (b) 21 (c) 23 (d) 22
  34. 34.What is the missing term in the AP 12, ?, 26, 33, 40? (a) 20 (b) 19 (c) 18 (d) 26
  35. 35.What is the missing term in the AP 3, ?, 7, 9, 11? (a) 7 (b) 5 (c) 4 (d) 6
  36. 36.Which term of the AP 2, 5, 8, 11, … is 53? (a) 17th (b) 18th (c) 20th (d) 19th
  37. 37.What is the 14th term of the AP 12, 16, 20, 24, …? (a) 64 (b) 56 (c) 52 (d) 68
  38. 38.Which term of the AP 18, 24, 30, 36, … is 234? (a) 36th (b) 38th (c) 39th (d) 37th
  39. 39.What is the 36th term of the AP 19, 25, 31, 37, …? (a) 210 (b) 229 (c) 216 (d) 235
  40. 40.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 31 (b) 8 (c) 30 (d) 60

Answer key

  1. 324
  2. 13
  3. 45
  4. 49
  5. 228
  6. 140
  7. 49
  8. 278
  9. 400
  10. 418
  11. 20th
  12. 492
  13. 144
  14. 98
  15. 414
  16. 12th
  17. 91
  18. 3321
  19. 13th
  20. 300
  21. 308
  22. 10th
  23. 363
  24. 225
  25. 71
  26. 105
  27. 25
  28. 135
  29. 201
  30. 122
  31. 12th
  32. 120
  33. 22
  34. 19
  35. 5
  36. 18th
  37. 64
  38. 37th
  39. 229
  40. 30

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