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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 962 · 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 12 terms of the AP 1, 4, 7, …? (a) 228 (b) 34 (c) 210 (d) 420
  2. 2.What is the 16th term of the AP 19, 27, 35, 43, …? (a) 128 (b) 120 (c) 147 (d) 139
  3. 3.What is the sum of all the whole numbers from 1 to 37? (a) 666 (b) 703 (c) 1406 (d) 704
  4. 4.What is the missing term in the AP 13, 18, 23, ?, 33? (a) 27 (b) 33 (c) 28 (d) 29
  5. 5.What is the 15th term of the AP 12, 15, 18, 21, …? (a) 45 (b) 54 (c) 57 (d) 42
  6. 6.What is the sum of the first 9 terms of the AP 5, 9, 13, …? (a) 207 (b) 378 (c) 37 (d) 189
  7. 7.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 12 (b) 60 (c) 114 (d) 57
  8. 8.What is the sum of the first 11 terms of the AP 2, 5, 8, …? (a) 190 (b) 374 (c) 32 (d) 187
  9. 9.What is the sum of the first 11 terms of the AP 9, 10, 11, …? (a) 155 (b) 154 (c) 308 (d) 19
  10. 10.Which term of the AP 1, 7, 13, 19, … is 49? (a) 8th (b) 11th (c) 9th (d) 10th
  11. 11.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 436 (c) 406 (d) 435
  12. 12.Which term of the AP 11, 15, 19, 23, … is 155? (a) 39th (b) 38th (c) 37th (d) 36th
  13. 13.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 27 (b) 374 (c) 198 (d) 187
  14. 14.What is the 12th term of the AP 2, 4, 6, 8, …? (a) 26 (b) 25 (c) 22 (d) 24
  15. 15.Which term of the AP 4, 10, 16, 22, … is 220? (a) 36th (b) 38th (c) 39th (d) 37th
  16. 16.What is the missing term in the AP 8, 11, ?, 17, 20? (a) 13 (b) 15 (c) 17 (d) 14
  17. 17.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 171 (c) 35 (d) 342
  18. 18.What is the missing term in the AP 5, 11, ?, 23, 29? (a) 17 (b) 23 (c) 16 (d) 18
  19. 19.What is the 29th term of the AP 3, 8, 13, 18, …? (a) 148 (b) 143 (c) 140 (d) 145
  20. 20.What is the 21st term of the AP 9, 12, 15, 18, …? (a) 63 (b) 69 (c) 60 (d) 72
  21. 21.What is the missing term in the AP 2, 11, ?, 29, 38? (a) 20 (b) 21 (c) 29 (d) 19
  22. 22.What is the 11th term of the AP 11, 16, 21, 26, …? (a) 61 (b) 55 (c) 66 (d) 50
  23. 23.What is the 16th term of the AP 3, 12, 21, 30, …? (a) 135 (b) 138 (c) 144 (d) 147
  24. 24.What is the 21st term of the AP 14, 23, 32, 41, …? (a) 203 (b) 189 (c) 194 (d) 180
  25. 25.What is the sum of the first 7 terms of the AP 9, 13, 17, …? (a) 33 (b) 161 (c) 294 (d) 147
  26. 26.What is the 15th term of the AP 20, 29, 38, 47, …? (a) 135 (b) 126 (c) 155 (d) 146
  27. 27.Which term of the AP 5, 10, 15, 20, … is 110? (a) 21st (b) 24th (c) 23rd (d) 22nd
  28. 28.What is the sum of the first 12 terms of the AP 3, 8, 13, …? (a) 366 (b) 58 (c) 732 (d) 396
  29. 29.What is the 31st term of the AP 4, 6, 8, 10, …? (a) 66 (b) 62 (c) 64 (d) 60
  30. 30.What is the sum of all the whole numbers from 1 to 65? (a) 2080 (b) 2146 (c) 2145 (d) 4290
  31. 31.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 16 (b) 92 (c) 91 (d) 182
  32. 32.What is the sum of all the whole numbers from 1 to 86? (a) 3741 (b) 3698 (c) 3655 (d) 7482
  33. 33.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 684 (b) 56 (c) 342 (d) 372
  34. 34.Which term of the AP 6, 13, 20, 27, … is 195? (a) 27th (b) 28th (c) 30th (d) 29th
  35. 35.What is the 32nd term of the AP 8, 17, 26, 35, …? (a) 279 (b) 288 (c) 296 (d) 287
  36. 36.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 3828 (c) 7832 (d) 3916
  37. 37.What is the sum of all the whole numbers from 1 to 81? (a) 6642 (b) 3321 (c) 3322 (d) 3240
  38. 38.What is the 16th term of the AP 11, 14, 17, 20, …? (a) 59 (b) 56 (c) 48 (d) 45
  39. 39.What is the sum of the first 11 terms of the AP 9, 11, 13, …? (a) 29 (b) 220 (c) 418 (d) 209
  40. 40.What is the 31st term of the AP 7, 11, 15, 19, …? (a) 124 (b) 131 (c) 127 (d) 120

Answer key

  1. 210
  2. 139
  3. 703
  4. 28
  5. 54
  6. 189
  7. 57
  8. 187
  9. 154
  10. 9th
  11. 435
  12. 37th
  13. 187
  14. 24
  15. 37th
  16. 14
  17. 324
  18. 17
  19. 143
  20. 69
  21. 20
  22. 61
  23. 138
  24. 194
  25. 147
  26. 146
  27. 22nd
  28. 366
  29. 64
  30. 2145
  31. 91
  32. 3741
  33. 342
  34. 28th
  35. 287
  36. 3916
  37. 3321
  38. 56
  39. 209
  40. 127

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