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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 984 · 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 2, 4, 6, …? (a) 24 (b) 312 (c) 156 (d) 168
  2. 2.What is the 32nd term of the AP 6, 9, 12, 15, …? (a) 96 (b) 99 (c) 102 (d) 93
  3. 3.What is the sum of the first 10 terms of the AP 4, 8, 12, …? (a) 220 (b) 240 (c) 40 (d) 440
  4. 4.What is the missing term in the AP 7, 10, 13, ?, 19? (a) 19 (b) 17 (c) 15 (d) 16
  5. 5.What is the missing term in the AP 10, 16, ?, 28, 34? (a) 28 (b) 23 (c) 22 (d) 21
  6. 6.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 49 (c) 28 (d) 13
  7. 7.What is the sum of the first 7 terms of the AP 4, 5, 6, …? (a) 50 (b) 49 (c) 10 (d) 98
  8. 8.Which term of the AP 7, 15, 23, 31, … is 159? (a) 21st (b) 19th (c) 20th (d) 22nd
  9. 9.What is the missing term in the AP 18, 22, 26, ?, 34? (a) 31 (b) 29 (c) 34 (d) 30
  10. 10.What is the 10th term of the AP 2, 5, 8, 11, …? (a) 30 (b) 29 (c) 32 (d) 27
  11. 11.Which term of the AP 12, 21, 30, 39, … is 138? (a) 15th (b) 14th (c) 17th (d) 16th
  12. 12.What is the missing term in the AP 5, 9, 13, ?, 21? (a) 16 (b) 21 (c) 17 (d) 18
  13. 13.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 198 (b) 27 (c) 374 (d) 187
  14. 14.What is the sum of all the whole numbers from 1 to 59? (a) 1770 (b) 1711 (c) 1771 (d) 3540
  15. 15.Which term of the AP 11, 16, 21, 26, … is 116? (a) 21st (b) 23rd (c) 22nd (d) 24th
  16. 16.What is the missing term in the AP 15, 17, 19, ?, 23? (a) 20 (b) 22 (c) 23 (d) 21
  17. 17.What is the sum of the first 8 terms of the AP 6, 7, 8, …? (a) 80 (b) 13 (c) 76 (d) 152
  18. 18.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 45 (b) 90 (c) 55 (d) 17
  19. 19.What is the sum of all the whole numbers from 1 to 81? (a) 3322 (b) 3240 (c) 6642 (d) 3321
  20. 20.What is the sum of all the whole numbers from 1 to 18? (a) 342 (b) 171 (c) 153 (d) 162
  21. 21.What is the 12th term of the AP 18, 27, 36, 45, …? (a) 117 (b) 99 (c) 108 (d) 126
  22. 22.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 190 (c) 380 (d) 171
  23. 23.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 378 (c) 351 (d) 756
  24. 24.What is the 32nd term of the AP 17, 25, 33, 41, …? (a) 273 (b) 248 (c) 265 (d) 256
  25. 25.What is the sum of the first 7 terms of the AP 4, 10, 16, …? (a) 175 (b) 40 (c) 308 (d) 154
  26. 26.What is the missing term in the AP 2, 4, 6, ?, 10? (a) 10 (b) 7 (c) 9 (d) 8
  27. 27.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 120 (c) 29 (d) 225
  28. 28.Which term of the AP 9, 11, 13, 15, … is 27? (a) 11th (b) 9th (c) 12th (d) 10th
  29. 29.What is the sum of the first 11 terms of the AP 3, 5, 7, …? (a) 154 (b) 286 (c) 23 (d) 143
  30. 30.What is the 20th term of the AP 1, 3, 5, 7, …? (a) 41 (b) 38 (c) 40 (d) 39
  31. 31.What is the 18th term of the AP 6, 9, 12, 15, …? (a) 60 (b) 51 (c) 54 (d) 57
  32. 32.What is the 16th term of the AP 20, 26, 32, 38, …? (a) 90 (b) 96 (c) 110 (d) 116
  33. 33.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 256 (c) 31 (d) 272
  34. 34.What is the 14th term of the AP 3, 10, 17, 24, …? (a) 91 (b) 98 (c) 101 (d) 94
  35. 35.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 231 (c) 441 (d) 41
  36. 36.What is the missing term in the AP 15, ?, 27, 33, 39? (a) 27 (b) 21 (c) 22 (d) 20
  37. 37.What is the 38th term of the AP 13, 21, 29, 37, …? (a) 296 (b) 304 (c) 309 (d) 317
  38. 38.What is the sum of all the whole numbers from 1 to 48? (a) 2352 (b) 1152 (c) 1176 (d) 1128
  39. 39.What is the sum of the first 7 terms of the AP 7, 10, 13, …? (a) 115 (b) 25 (c) 224 (d) 112
  40. 40.What is the 18th term of the AP 12, 19, 26, 33, …? (a) 138 (b) 119 (c) 126 (d) 131

Answer key

  1. 156
  2. 99
  3. 220
  4. 16
  5. 22
  6. 49
  7. 49
  8. 20th
  9. 30
  10. 29
  11. 15th
  12. 17
  13. 187
  14. 1770
  15. 22nd
  16. 21
  17. 76
  18. 45
  19. 3321
  20. 171
  21. 117
  22. 190
  23. 378
  24. 265
  25. 154
  26. 8
  27. 225
  28. 10th
  29. 143
  30. 39
  31. 57
  32. 110
  33. 256
  34. 94
  35. 441
  36. 21
  37. 309
  38. 1176
  39. 112
  40. 131

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