← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 469 · 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 71? (a) 2557 (b) 2485 (c) 5112 (d) 2556
  2. 2.What is the sum of all the whole numbers from 1 to 78? (a) 3081 (b) 3003 (c) 6162 (d) 3042
  3. 3.What is the sum of the first 9 terms of the AP 5, 11, 17, …? (a) 288 (b) 261 (c) 53 (d) 522
  4. 4.What is the missing term in the AP 9, 17, ?, 33, 41? (a) 26 (b) 25 (c) 33 (d) 24
  5. 5.What is the missing term in the AP 13, ?, 17, 19, 21? (a) 17 (b) 15 (c) 14 (d) 16
  6. 6.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 858 (b) 462 (c) 429 (d) 69
  7. 7.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 24 (b) 108 (c) 120 (d) 216
  8. 8.What is the sum of all the whole numbers from 1 to 25? (a) 650 (b) 326 (c) 300 (d) 325
  9. 9.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 21 (b) 42 (c) 6 (d) 24
  10. 10.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 406 (c) 812 (d) 378
  11. 11.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 99 (b) 198 (c) 24 (d) 108
  12. 12.What is the 32nd term of the AP 11, 18, 25, 32, …? (a) 224 (b) 228 (c) 217 (d) 235
  13. 13.What is the 16th term of the AP 14, 22, 30, 38, …? (a) 142 (b) 120 (c) 128 (d) 134
  14. 14.What is the missing term in the AP 3, 11, ?, 27, 35? (a) 27 (b) 18 (c) 20 (d) 19
  15. 15.What is the 35th term of the AP 11, 20, 29, 38, …? (a) 326 (b) 306 (c) 317 (d) 315
  16. 16.What is the missing term in the AP 9, 13, 17, ?, 25? (a) 22 (b) 25 (c) 20 (d) 21
  17. 17.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 9 (b) 78 (c) 39 (d) 42
  18. 18.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 57 (b) 354 (c) 708 (d) 384
  19. 19.What is the 19th term of the AP 20, 25, 30, 35, …? (a) 95 (b) 90 (c) 110 (d) 115
  20. 20.What is the sum of the first 7 terms of the AP 9, 12, 15, …? (a) 126 (b) 252 (c) 129 (d) 27
  21. 21.What is the missing term in the AP 2, 6, ?, 14, 18? (a) 9 (b) 11 (c) 10 (d) 14
  22. 22.What is the 13th term of the AP 11, 13, 15, 17, …? (a) 37 (b) 35 (c) 26 (d) 24
  23. 23.What is the 20th term of the AP 17, 20, 23, 26, …? (a) 57 (b) 74 (c) 60 (d) 77
  24. 24.What is the missing term in the AP 10, ?, 26, 34, 42? (a) 19 (b) 26 (c) 17 (d) 18
  25. 25.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 192 (b) 31 (c) 114 (d) 96
  26. 26.What is the sum of the first 10 terms of the AP 1, 7, 13, …? (a) 55 (b) 560 (c) 280 (d) 310
  27. 27.What is the sum of all the whole numbers from 1 to 48? (a) 1176 (b) 1152 (c) 2352 (d) 1128
  28. 28.What is the 33rd term of the AP 2, 9, 16, 23, …? (a) 224 (b) 226 (c) 233 (d) 231
  29. 29.What is the sum of the first 8 terms of the AP 10, 16, 22, …? (a) 496 (b) 272 (c) 248 (d) 52
  30. 30.What is the sum of the first 9 terms of the AP 4, 9, 14, …? (a) 432 (b) 216 (c) 44 (d) 221
  31. 31.What is the 36th term of the AP 4, 9, 14, 19, …? (a) 175 (b) 180 (c) 179 (d) 184
  32. 32.What is the sum of the first 9 terms of the AP 4, 10, 16, …? (a) 52 (b) 504 (c) 252 (d) 279
  33. 33.Which term of the AP 13, 20, 27, 34, … is 188? (a) 27th (b) 26th (c) 25th (d) 28th
  34. 34.What is the 12th term of the AP 17, 24, 31, 38, …? (a) 84 (b) 77 (c) 94 (d) 101
  35. 35.What is the missing term in the AP 14, ?, 30, 38, 46? (a) 21 (b) 22 (c) 30 (d) 23
  36. 36.Which term of the AP 9, 14, 19, 24, … is 154? (a) 29th (b) 32nd (c) 30th (d) 31st
  37. 37.What is the 26th term of the AP 7, 10, 13, 16, …? (a) 85 (b) 75 (c) 78 (d) 82
  38. 38.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 576 (c) 47 (d) 600
  39. 39.What is the 23rd term of the AP 2, 5, 8, 11, …? (a) 71 (b) 66 (c) 69 (d) 68
  40. 40.Which term of the AP 12, 16, 20, 24, … is 80? (a) 20th (b) 17th (c) 19th (d) 18th

Answer key

  1. 2556
  2. 3081
  3. 261
  4. 25
  5. 15
  6. 429
  7. 108
  8. 325
  9. 21
  10. 406
  11. 99
  12. 228
  13. 134
  14. 19
  15. 317
  16. 21
  17. 39
  18. 354
  19. 110
  20. 126
  21. 10
  22. 35
  23. 74
  24. 18
  25. 96
  26. 280
  27. 1176
  28. 226
  29. 248
  30. 216
  31. 179
  32. 252
  33. 26th
  34. 94
  35. 22
  36. 30th
  37. 82
  38. 576
  39. 68
  40. 18th

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad