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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 577 · 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 20th term of the AP 6, 15, 24, 33, …? (a) 186 (b) 177 (c) 180 (d) 171
  2. 2.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 32 (b) 252 (c) 264 (d) 504
  3. 3.What is the missing term in the AP 5, 9, ?, 17, 21? (a) 14 (b) 13 (c) 17 (d) 12
  4. 4.What is the 14th term of the AP 20, 25, 30, 35, …? (a) 90 (b) 85 (c) 65 (d) 70
  5. 5.Which term of the AP 17, 25, 33, 41, … is 137? (a) 16th (b) 18th (c) 15th (d) 17th
  6. 6.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 45 (c) 529 (d) 276
  7. 7.What is the missing term in the AP 3, ?, 9, 12, 15? (a) 9 (b) 6 (c) 5 (d) 7
  8. 8.What is the sum of all the whole numbers from 1 to 31? (a) 497 (b) 992 (c) 496 (d) 465
  9. 9.What is the sum of all the whole numbers from 1 to 43? (a) 946 (b) 903 (c) 1892 (d) 947
  10. 10.What is the 21st term of the AP 16, 19, 22, 25, …? (a) 63 (b) 60 (c) 79 (d) 76
  11. 11.What is the sum of all the whole numbers from 1 to 55? (a) 1541 (b) 1485 (c) 3080 (d) 1540
  12. 12.What is the sum of all the whole numbers from 1 to 32? (a) 496 (b) 1056 (c) 528 (d) 512
  13. 13.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 60 (b) 57 (c) 114 (d) 12
  14. 14.What is the 24th term of the AP 5, 11, 17, 23, …? (a) 149 (b) 144 (c) 138 (d) 143
  15. 15.What is the sum of all the whole numbers from 1 to 27? (a) 756 (b) 378 (c) 351 (d) 379
  16. 16.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 15 (c) 9 (d) 30
  17. 17.What is the missing term in the AP 14, 18, ?, 26, 30? (a) 26 (b) 21 (c) 23 (d) 22
  18. 18.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 13 (b) 35 (c) 70 (d) 38
  19. 19.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 70 (b) 17 (c) 65 (d) 130
  20. 20.What is the 12th term of the AP 8, 10, 12, 14, …? (a) 24 (b) 30 (c) 32 (d) 22
  21. 21.What is the sum of the first 7 terms of the AP 10, 15, 20, …? (a) 180 (b) 175 (c) 40 (d) 350
  22. 22.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 17 (b) 80 (c) 88 (d) 160
  23. 23.What is the sum of all the whole numbers from 1 to 54? (a) 1458 (b) 2970 (c) 1485 (d) 1431
  24. 24.What is the sum of all the whole numbers from 1 to 22? (a) 242 (b) 231 (c) 253 (d) 506
  25. 25.What is the sum of all the whole numbers from 1 to 18? (a) 153 (b) 171 (c) 342 (d) 162
  26. 26.Which term of the AP 11, 20, 29, 38, … is 101? (a) 10th (b) 11th (c) 12th (d) 13th
  27. 27.What is the sum of all the whole numbers from 1 to 90? (a) 4050 (b) 4005 (c) 4095 (d) 8190
  28. 28.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 441 (c) 41 (d) 231
  29. 29.What is the missing term in the AP 13, ?, 17, 19, 21? (a) 14 (b) 16 (c) 17 (d) 15
  30. 30.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 66 (b) 13 (c) 126 (d) 63
  31. 31.What is the 13th term of the AP 18, 22, 26, 30, …? (a) 66 (b) 70 (c) 48 (d) 52
  32. 32.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 85 (b) 150 (c) 75 (d) 23
  33. 33.What is the 34th term of the AP 4, 9, 14, 19, …? (a) 170 (b) 165 (c) 169 (d) 174
  34. 34.What is the missing term in the AP 17, 19, 21, ?, 25? (a) 23 (b) 22 (c) 25 (d) 24
  35. 35.What is the 34th term of the AP 5, 14, 23, 32, …? (a) 302 (b) 311 (c) 306 (d) 297
  36. 36.What is the missing term in the AP 5, 7, ?, 11, 13? (a) 11 (b) 10 (c) 8 (d) 9
  37. 37.What is the sum of all the whole numbers from 1 to 65? (a) 4290 (b) 2146 (c) 2080 (d) 2145
  38. 38.What is the sum of the first 7 terms of the AP 7, 10, 13, …? (a) 224 (b) 25 (c) 115 (d) 112
  39. 39.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 13 (b) 176 (c) 88 (d) 89
  40. 40.Which term of the AP 4, 7, 10, 13, … is 94? (a) 30th (b) 31st (c) 33rd (d) 32nd

Answer key

  1. 177
  2. 252
  3. 13
  4. 85
  5. 16th
  6. 529
  7. 6
  8. 496
  9. 946
  10. 76
  11. 1540
  12. 528
  13. 57
  14. 143
  15. 378
  16. 25
  17. 22
  18. 35
  19. 65
  20. 30
  21. 175
  22. 80
  23. 1485
  24. 253
  25. 171
  26. 11th
  27. 4095
  28. 441
  29. 15
  30. 63
  31. 66
  32. 75
  33. 169
  34. 23
  35. 302
  36. 9
  37. 2145
  38. 112
  39. 88
  40. 31st

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