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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 139 · 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 6 terms of the AP 1, 4, 7, …? (a) 16 (b) 51 (c) 102 (d) 60
  2. 2.What is the 31st term of the AP 18, 24, 30, 36, …? (a) 186 (b) 198 (c) 204 (d) 180
  3. 3.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 72 (b) 40 (c) 36 (d) 8
  4. 4.What is the 38th term of the AP 8, 12, 16, 20, …? (a) 148 (b) 156 (c) 152 (d) 160
  5. 5.What is the sum of the first 11 terms of the AP 9, 14, 19, …? (a) 748 (b) 379 (c) 374 (d) 59
  6. 6.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 190 (b) 200 (c) 28 (d) 380
  7. 7.What is the missing term in the AP 3, ?, 7, 9, 11? (a) 6 (b) 7 (c) 4 (d) 5
  8. 8.What is the sum of the first 9 terms of the AP 7, 11, 15, …? (a) 414 (b) 225 (c) 39 (d) 207
  9. 9.What is the sum of all the whole numbers from 1 to 68? (a) 4692 (b) 2278 (c) 2312 (d) 2346
  10. 10.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 153 (b) 306 (c) 171 (d) 33
  11. 11.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 144 (d) 23
  12. 12.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 406 (c) 784 (d) 812
  13. 13.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 198 (b) 27 (c) 187 (d) 374
  14. 14.Which term of the AP 16, 24, 32, 40, … is 96? (a) 10th (b) 13th (c) 11th (d) 12th
  15. 15.What is the sum of the first 10 terms of the AP 4, 5, 6, …? (a) 170 (b) 13 (c) 90 (d) 85
  16. 16.What is the 38th term of the AP 10, 17, 24, 31, …? (a) 266 (b) 276 (c) 269 (d) 259
  17. 17.Which term of the AP 2, 11, 20, 29, … is 155? (a) 19th (b) 18th (c) 17th (d) 20th
  18. 18.What is the 26th term of the AP 1, 4, 7, 10, …? (a) 78 (b) 76 (c) 79 (d) 75
  19. 19.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 286 (b) 308 (c) 572 (d) 46
  20. 20.Which term of the AP 4, 6, 8, 10, … is 52? (a) 25th (b) 24th (c) 26th (d) 27th
  21. 21.What is the sum of all the whole numbers from 1 to 72? (a) 2628 (b) 2592 (c) 2556 (d) 5256
  22. 22.What is the sum of all the whole numbers from 1 to 44? (a) 946 (b) 1980 (c) 990 (d) 968
  23. 23.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 342 (c) 35 (d) 171
  24. 24.Which term of the AP 18, 20, 22, 24, … is 74? (a) 28th (b) 37th (c) 30th (d) 29th
  25. 25.What is the sum of all the whole numbers from 1 to 54? (a) 1431 (b) 2970 (c) 1458 (d) 1485
  26. 26.What is the 21st term of the AP 2, 7, 12, 17, …? (a) 107 (b) 105 (c) 100 (d) 102
  27. 27.What is the 18th term of the AP 2, 8, 14, 20, …? (a) 104 (b) 102 (c) 110 (d) 108
  28. 28.Which term of the AP 11, 15, 19, 23, … is 91? (a) 22nd (b) 23rd (c) 20th (d) 21st
  29. 29.What is the sum of all the whole numbers from 1 to 76? (a) 2926 (b) 2850 (c) 5852 (d) 2888
  30. 30.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 17 (c) 90 (d) 45
  31. 31.What is the 40th term of the AP 6, 8, 10, 12, …? (a) 84 (b) 80 (c) 86 (d) 78
  32. 32.What is the 14th term of the AP 5, 10, 15, 20, …? (a) 75 (b) 65 (c) 70 (d) 71
  33. 33.What is the sum of all the whole numbers from 1 to 35? (a) 595 (b) 631 (c) 1260 (d) 630
  34. 34.What is the sum of all the whole numbers from 1 to 83? (a) 6972 (b) 3487 (c) 3486 (d) 3403
  35. 35.What is the sum of all the whole numbers from 1 to 74? (a) 2738 (b) 2775 (c) 2701 (d) 5550
  36. 36.What is the sum of the first 9 terms of the AP 5, 11, 17, …? (a) 522 (b) 261 (c) 53 (d) 288
  37. 37.What is the 38th term of the AP 20, 25, 30, 35, …? (a) 185 (b) 205 (c) 190 (d) 210
  38. 38.What is the 19th term of the AP 16, 22, 28, 34, …? (a) 108 (b) 114 (c) 130 (d) 124
  39. 39.Which term of the AP 10, 14, 18, 22, … is 122? (a) 28th (b) 31st (c) 29th (d) 30th
  40. 40.What is the 36th term of the AP 6, 11, 16, 21, …? (a) 181 (b) 180 (c) 175 (d) 186

Answer key

  1. 51
  2. 198
  3. 36
  4. 156
  5. 374
  6. 190
  7. 5
  8. 207
  9. 2346
  10. 153
  11. 144
  12. 784
  13. 187
  14. 11th
  15. 85
  16. 269
  17. 18th
  18. 76
  19. 286
  20. 25th
  21. 2628
  22. 990
  23. 324
  24. 29th
  25. 1485
  26. 102
  27. 104
  28. 21st
  29. 2926
  30. 81
  31. 84
  32. 70
  33. 630
  34. 3486
  35. 2775
  36. 261
  37. 205
  38. 124
  39. 29th
  40. 181

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