← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 294 · 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 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 240 (c) 120 (d) 225
  2. 2.What is the sum of all the whole numbers from 1 to 64? (a) 2080 (b) 4160 (c) 2048 (d) 2016
  3. 3.What is the 15th term of the AP 5, 8, 11, 14, …? (a) 42 (b) 47 (c) 50 (d) 45
  4. 4.What is the 38th term of the AP 13, 18, 23, 28, …? (a) 190 (b) 198 (c) 185 (d) 203
  5. 5.What is the 16th term of the AP 13, 20, 27, 34, …? (a) 112 (b) 125 (c) 105 (d) 118
  6. 6.What is the 22nd term of the AP 3, 6, 9, 12, …? (a) 63 (b) 66 (c) 67 (d) 69
  7. 7.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 31 (c) 272 (d) 256
  8. 8.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 91 (c) 92 (d) 78
  9. 9.What is the 23rd term of the AP 16, 18, 20, 22, …? (a) 62 (b) 60 (c) 44 (d) 46
  10. 10.What is the sum of the first 7 terms of the AP 5, 6, 7, …? (a) 11 (b) 112 (c) 57 (d) 56
  11. 11.What is the 28th term of the AP 17, 21, 25, 29, …? (a) 125 (b) 108 (c) 129 (d) 112
  12. 12.What is the sum of the first 7 terms of the AP 1, 5, 9, …? (a) 105 (b) 91 (c) 182 (d) 25
  13. 13.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 186 (b) 21 (c) 372 (d) 192
  14. 14.What is the 22nd term of the AP 20, 24, 28, 32, …? (a) 108 (b) 84 (c) 104 (d) 88
  15. 15.What is the 33rd term of the AP 3, 7, 11, 15, …? (a) 128 (b) 135 (c) 131 (d) 132
  16. 16.What is the sum of all the whole numbers from 1 to 82? (a) 3403 (b) 3321 (c) 6806 (d) 3362
  17. 17.What is the 17th term of the AP 4, 9, 14, 19, …? (a) 89 (b) 80 (c) 85 (d) 84
  18. 18.What is the sum of all the whole numbers from 1 to 93? (a) 4278 (b) 4372 (c) 8742 (d) 4371
  19. 19.What is the sum of all the whole numbers from 1 to 86? (a) 3655 (b) 3741 (c) 3698 (d) 7482
  20. 20.What is the sum of the first 12 terms of the AP 4, 9, 14, …? (a) 59 (b) 378 (c) 756 (d) 408
  21. 21.What is the 26th term of the AP 2, 9, 16, 23, …? (a) 182 (b) 175 (c) 177 (d) 184
  22. 22.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 174 (b) 20 (c) 180 (d) 348
  23. 23.What is the sum of all the whole numbers from 1 to 51? (a) 1275 (b) 1326 (c) 2652 (d) 1327
  24. 24.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 15 (b) 16 (c) 5 (d) 30
  25. 25.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 420 (c) 39 (d) 210
  26. 26.What is the 30th term of the AP 16, 18, 20, 22, …? (a) 60 (b) 74 (c) 76 (d) 58
  27. 27.What is the 23rd term of the AP 8, 11, 14, 17, …? (a) 77 (b) 66 (c) 69 (d) 74
  28. 28.What is the 22nd term of the AP 13, 22, 31, 40, …? (a) 189 (b) 198 (c) 202 (d) 211
  29. 29.What is the missing term in the AP 4, ?, 8, 10, 12? (a) 8 (b) 5 (c) 6 (d) 7
  30. 30.What is the sum of all the whole numbers from 1 to 49? (a) 1225 (b) 1226 (c) 2450 (d) 1176
  31. 31.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 324 (c) 342 (d) 35
  32. 32.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 253 (b) 506 (c) 275 (d) 43
  33. 33.What is the sum of all the whole numbers from 1 to 96? (a) 4608 (b) 4560 (c) 9312 (d) 4656
  34. 34.What is the 14th term of the AP 4, 8, 12, 16, …? (a) 60 (b) 52 (c) 57 (d) 56
  35. 35.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 110 (b) 190 (c) 31 (d) 95
  36. 36.What is the sum of all the whole numbers from 1 to 75? (a) 2850 (b) 5700 (c) 2851 (d) 2775
  37. 37.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 11 (b) 40 (c) 70 (d) 35
  38. 38.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 78 (b) 154 (c) 14 (d) 77
  39. 39.What is the sum of the first 9 terms of the AP 8, 14, 20, …? (a) 288 (b) 56 (c) 576 (d) 315
  40. 40.What is the sum of all the whole numbers from 1 to 48? (a) 1176 (b) 2352 (c) 1128 (d) 1152

Answer key

  1. 225
  2. 2080
  3. 47
  4. 198
  5. 118
  6. 66
  7. 256
  8. 91
  9. 60
  10. 56
  11. 125
  12. 91
  13. 186
  14. 104
  15. 131
  16. 3403
  17. 84
  18. 4371
  19. 3741
  20. 378
  21. 177
  22. 174
  23. 1326
  24. 15
  25. 400
  26. 74
  27. 74
  28. 202
  29. 6
  30. 1225
  31. 324
  32. 253
  33. 4656
  34. 56
  35. 95
  36. 2850
  37. 35
  38. 77
  39. 288
  40. 1176

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