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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 868 · 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 24th term of the AP 15, 24, 33, 42, …? (a) 216 (b) 231 (c) 207 (d) 222
  2. 2.What is the sum of all the whole numbers from 1 to 55? (a) 1540 (b) 3080 (c) 1541 (d) 1485
  3. 3.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 600 (c) 300 (d) 576
  4. 4.What is the 26th term of the AP 13, 15, 17, 19, …? (a) 63 (b) 52 (c) 65 (d) 50
  5. 5.Which term of the AP 15, 21, 27, 33, … is 147? (a) 22nd (b) 25th (c) 24th (d) 23rd
  6. 6.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 156 (c) 144 (d) 78
  7. 7.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 110 (b) 15 (c) 111 (d) 220
  8. 8.Which term of the AP 19, 21, 23, 25, … is 81? (a) 32nd (b) 33rd (c) 31st (d) 34th
  9. 9.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 506 (c) 253 (d) 484
  10. 10.What is the sum of all the whole numbers from 1 to 65? (a) 2146 (b) 4290 (c) 2080 (d) 2145
  11. 11.What is the 32nd term of the AP 11, 14, 17, 20, …? (a) 93 (b) 107 (c) 96 (d) 104
  12. 12.What is the missing term in the AP 4, 9, ?, 19, 24? (a) 14 (b) 19 (c) 15 (d) 13
  13. 13.What is the sum of all the whole numbers from 1 to 27? (a) 756 (b) 379 (c) 378 (d) 351
  14. 14.What is the missing term in the AP 17, 26, ?, 44, 53? (a) 36 (b) 34 (c) 44 (d) 35
  15. 15.What is the sum of all the whole numbers from 1 to 57? (a) 1596 (b) 1653 (c) 3306 (d) 1654
  16. 16.What is the 18th term of the AP 5, 14, 23, 32, …? (a) 158 (b) 153 (c) 167 (d) 162
  17. 17.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 225 (d) 240
  18. 18.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 406 (c) 436 (d) 435
  19. 19.What is the 31st term of the AP 8, 10, 12, 14, …? (a) 62 (b) 60 (c) 70 (d) 68
  20. 20.What is the sum of the first 7 terms of the AP 7, 13, 19, …? (a) 175 (b) 196 (c) 43 (d) 350
  21. 21.Which term of the AP 12, 19, 26, 33, … is 96? (a) 13th (b) 12th (c) 14th (d) 15th
  22. 22.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 29 (b) 100 (c) 170 (d) 85
  23. 23.Which term of the AP 13, 16, 19, 22, … is 37? (a) 9th (b) 8th (c) 11th (d) 10th
  24. 24.What is the 34th term of the AP 20, 27, 34, 41, …? (a) 238 (b) 251 (c) 231 (d) 258
  25. 25.Which term of the AP 5, 8, 11, 14, … is 47? (a) 14th (b) 15th (c) 16th (d) 17th
  26. 26.What is the sum of all the whole numbers from 1 to 48? (a) 2352 (b) 1176 (c) 1128 (d) 1152
  27. 27.What is the 13th term of the AP 18, 21, 24, 27, …? (a) 36 (b) 39 (c) 54 (d) 57
  28. 28.What is the missing term in the AP 16, ?, 22, 25, 28? (a) 18 (b) 22 (c) 19 (d) 20
  29. 29.What is the 26th term of the AP 1, 3, 5, 7, …? (a) 51 (b) 50 (c) 52 (d) 53
  30. 30.What is the sum of all the whole numbers from 1 to 93? (a) 4371 (b) 4278 (c) 4372 (d) 8742
  31. 31.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 41 (c) 441 (d) 231
  32. 32.What is the 21st term of the AP 11, 16, 21, 26, …? (a) 111 (b) 116 (c) 100 (d) 105
  33. 33.What is the 11th term of the AP 3, 6, 9, 12, …? (a) 36 (b) 30 (c) 34 (d) 33
  34. 34.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 60 (b) 14 (c) 108 (d) 54
  35. 35.What is the missing term in the AP 14, 19, 24, ?, 34? (a) 34 (b) 28 (c) 30 (d) 29
  36. 36.What is the 21st term of the AP 9, 17, 25, 33, …? (a) 168 (b) 160 (c) 169 (d) 177
  37. 37.What is the sum of all the whole numbers from 1 to 26? (a) 351 (b) 338 (c) 702 (d) 325
  38. 38.What is the sum of all the whole numbers from 1 to 94? (a) 8930 (b) 4465 (c) 4418 (d) 4371
  39. 39.What is the 28th term of the AP 15, 22, 29, 36, …? (a) 211 (b) 196 (c) 189 (d) 204
  40. 40.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 5050 (c) 5000 (d) 10100

Answer key

  1. 222
  2. 1540
  3. 576
  4. 63
  5. 23rd
  6. 144
  7. 110
  8. 32nd
  9. 484
  10. 2145
  11. 104
  12. 14
  13. 378
  14. 35
  15. 1653
  16. 158
  17. 225
  18. 435
  19. 68
  20. 175
  21. 13th
  22. 85
  23. 9th
  24. 251
  25. 15th
  26. 1176
  27. 54
  28. 19
  29. 51
  30. 4371
  31. 441
  32. 111
  33. 33
  34. 54
  35. 29
  36. 169
  37. 351
  38. 4465
  39. 204
  40. 5050

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