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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 810 · 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 11 terms of the AP 1, 5, 9, …? (a) 41 (b) 253 (c) 462 (d) 231
  2. 2.What is the sum of all the whole numbers from 1 to 87? (a) 3829 (b) 3741 (c) 7656 (d) 3828
  3. 3.Which term of the AP 9, 18, 27, 36, … is 117? (a) 14th (b) 12th (c) 15th (d) 13th
  4. 4.Which term of the AP 18, 24, 30, 36, … is 90? (a) 15th (b) 13th (c) 12th (d) 14th
  5. 5.What is the sum of the first 9 terms of the AP 8, 11, 14, …? (a) 360 (b) 183 (c) 32 (d) 180
  6. 6.What is the 19th term of the AP 12, 14, 16, 18, …? (a) 36 (b) 48 (c) 38 (d) 50
  7. 7.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 17 (d) 81
  8. 8.What is the 25th term of the AP 20, 22, 24, 26, …? (a) 68 (b) 48 (c) 50 (d) 70
  9. 9.What is the 11th term of the AP 16, 19, 22, 25, …? (a) 46 (b) 33 (c) 30 (d) 49
  10. 10.What is the 14th term of the AP 10, 19, 28, 37, …? (a) 117 (b) 127 (c) 126 (d) 136
  11. 11.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 45 (b) 17 (c) 90 (d) 55
  12. 12.What is the 17th term of the AP 6, 9, 12, 15, …? (a) 54 (b) 51 (c) 48 (d) 57
  13. 13.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 43 (c) 506 (d) 253
  14. 14.Which term of the AP 11, 19, 27, 35, … is 139? (a) 17th (b) 18th (c) 16th (d) 19th
  15. 15.What is the 33rd term of the AP 2, 11, 20, 29, …? (a) 288 (b) 290 (c) 299 (d) 297
  16. 16.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 19 (c) 100 (d) 110
  17. 17.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 28 (c) 49 (d) 56
  18. 18.What is the 22nd term of the AP 2, 6, 10, 14, …? (a) 84 (b) 90 (c) 86 (d) 88
  19. 19.Which term of the AP 4, 8, 12, 16, … is 64? (a) 18th (b) 16th (c) 17th (d) 15th
  20. 20.What is the sum of all the whole numbers from 1 to 28? (a) 378 (b) 392 (c) 406 (d) 812
  21. 21.What is the sum of the first 9 terms of the AP 8, 13, 18, …? (a) 257 (b) 48 (c) 252 (d) 504
  22. 22.What is the missing term in the AP 18, ?, 34, 42, 50? (a) 25 (b) 26 (c) 27 (d) 34
  23. 23.What is the missing term in the AP 6, 15, 24, ?, 42? (a) 32 (b) 34 (c) 42 (d) 33
  24. 24.What is the sum of the first 9 terms of the AP 10, 16, 22, …? (a) 58 (b) 306 (c) 333 (d) 612
  25. 25.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 16 (b) 91 (c) 92 (d) 182
  26. 26.What is the sum of all the whole numbers from 1 to 23? (a) 276 (b) 552 (c) 277 (d) 253
  27. 27.What is the sum of all the whole numbers from 1 to 84? (a) 3570 (b) 3486 (c) 7140 (d) 3528
  28. 28.What is the sum of all the whole numbers from 1 to 47? (a) 1129 (b) 1081 (c) 1128 (d) 2256
  29. 29.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 270 (b) 490 (c) 47 (d) 245
  30. 30.Which term of the AP 18, 22, 26, 30, … is 90? (a) 19th (b) 21st (c) 20th (d) 18th
  31. 31.What is the missing term in the AP 20, ?, 38, 47, 56? (a) 28 (b) 38 (c) 29 (d) 30
  32. 32.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 260 (b) 470 (c) 46 (d) 235
  33. 33.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 48 (b) 90 (c) 10 (d) 45
  34. 34.Which term of the AP 1, 4, 7, 10, … is 55? (a) 20th (b) 19th (c) 18th (d) 21st
  35. 35.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 56 (b) 112 (c) 14 (d) 63
  36. 36.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 33 (c) 306 (d) 153
  37. 37.Which term of the AP 12, 20, 28, 36, … is 116? (a) 14th (b) 16th (c) 15th (d) 13th
  38. 38.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 35 (c) 171 (d) 324
  39. 39.Which term of the AP 9, 14, 19, 24, … is 44? (a) 9th (b) 10th (c) 8th (d) 7th
  40. 40.What is the sum of all the whole numbers from 1 to 99? (a) 4851 (b) 4950 (c) 4951 (d) 9900

Answer key

  1. 231
  2. 3828
  3. 13th
  4. 13th
  5. 180
  6. 48
  7. 81
  8. 68
  9. 46
  10. 127
  11. 45
  12. 54
  13. 484
  14. 17th
  15. 290
  16. 100
  17. 49
  18. 86
  19. 16th
  20. 406
  21. 252
  22. 26
  23. 33
  24. 306
  25. 91
  26. 276
  27. 3570
  28. 1128
  29. 245
  30. 19th
  31. 29
  32. 235
  33. 45
  34. 19th
  35. 56
  36. 289
  37. 14th
  38. 324
  39. 8th
  40. 4950

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