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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 387 · 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 13th term of the AP 9, 16, 23, 30, …? (a) 84 (b) 93 (c) 100 (d) 91
  2. 2.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 50 (b) 16 (c) 53 (d) 100
  3. 3.What is the 17th term of the AP 18, 21, 24, 27, …? (a) 69 (b) 51 (c) 48 (d) 66
  4. 4.What is the missing term in the AP 16, ?, 26, 31, 36? (a) 20 (b) 21 (c) 26 (d) 22
  5. 5.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 990 (c) 1035 (d) 2070
  6. 6.What is the sum of the first 10 terms of the AP 2, 5, 8, …? (a) 29 (b) 170 (c) 310 (d) 155
  7. 7.What is the sum of all the whole numbers from 1 to 46? (a) 1058 (b) 1035 (c) 2162 (d) 1081
  8. 8.What is the 12th term of the AP 5, 14, 23, 32, …? (a) 108 (b) 99 (c) 104 (d) 113
  9. 9.Which term of the AP 19, 27, 35, 43, … is 283? (a) 36th (b) 35th (c) 33rd (d) 34th
  10. 10.What is the sum of the first 12 terms of the AP 4, 10, 16, …? (a) 480 (b) 70 (c) 444 (d) 888
  11. 11.What is the missing term in the AP 11, ?, 19, 23, 27? (a) 14 (b) 16 (c) 15 (d) 19
  12. 12.What is the 35th term of the AP 11, 16, 21, 26, …? (a) 181 (b) 170 (c) 175 (d) 186
  13. 13.What is the 25th term of the AP 20, 29, 38, 47, …? (a) 236 (b) 225 (c) 245 (d) 216
  14. 14.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 240 (c) 225 (d) 29
  15. 15.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 306 (c) 154 (d) 136
  16. 16.What is the missing term in the AP 17, 23, ?, 35, 41? (a) 29 (b) 30 (c) 35 (d) 28
  17. 17.Which term of the AP 14, 17, 20, 23, … is 122? (a) 36th (b) 39th (c) 37th (d) 38th
  18. 18.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 182 (c) 169 (d) 25
  19. 19.What is the sum of the first 9 terms of the AP 4, 7, 10, …? (a) 288 (b) 28 (c) 144 (d) 147
  20. 20.What is the 31st term of the AP 17, 20, 23, 26, …? (a) 110 (b) 107 (c) 90 (d) 93
  21. 21.What is the sum of the first 9 terms of the AP 8, 11, 14, …? (a) 32 (b) 360 (c) 180 (d) 183
  22. 22.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 90 (b) 19 (c) 84 (d) 168
  23. 23.What is the sum of all the whole numbers from 1 to 70? (a) 4970 (b) 2450 (c) 2415 (d) 2485
  24. 24.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 400 (c) 39 (d) 210
  25. 25.Which term of the AP 4, 13, 22, 31, … is 337? (a) 38th (b) 37th (c) 39th (d) 40th
  26. 26.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 126 (b) 216 (c) 33 (d) 108
  27. 27.What is the 33rd term of the AP 3, 6, 9, 12, …? (a) 102 (b) 96 (c) 100 (d) 99
  28. 28.What is the sum of all the whole numbers from 1 to 90? (a) 4005 (b) 4050 (c) 4095 (d) 8190
  29. 29.Which term of the AP 5, 7, 9, 11, … is 49? (a) 22nd (b) 23rd (c) 25th (d) 24th
  30. 30.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 900 (c) 465 (d) 930
  31. 31.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 528 (c) 1056 (d) 496
  32. 32.What is the 14th term of the AP 13, 21, 29, 37, …? (a) 117 (b) 125 (c) 112 (d) 104
  33. 33.What is the missing term in the AP 6, 11, 16, ?, 26? (a) 26 (b) 20 (c) 22 (d) 21
  34. 34.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 702 (c) 351 (d) 676
  35. 35.What is the 26th term of the AP 5, 7, 9, 11, …? (a) 57 (b) 50 (c) 52 (d) 55
  36. 36.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 496 (c) 465 (d) 497
  37. 37.What is the missing term in the AP 20, 22, ?, 26, 28? (a) 26 (b) 25 (c) 23 (d) 24
  38. 38.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 432 (b) 228 (c) 29 (d) 216
  39. 39.What is the 34th term of the AP 9, 18, 27, 36, …? (a) 297 (b) 315 (c) 306 (d) 307
  40. 40.Which term of the AP 2, 8, 14, 20, … is 164? (a) 30th (b) 29th (c) 27th (d) 28th

Answer key

  1. 93
  2. 50
  3. 66
  4. 21
  5. 1035
  6. 155
  7. 1081
  8. 104
  9. 34th
  10. 444
  11. 15
  12. 181
  13. 236
  14. 225
  15. 153
  16. 29
  17. 37th
  18. 169
  19. 144
  20. 107
  21. 180
  22. 84
  23. 2485
  24. 400
  25. 38th
  26. 108
  27. 99
  28. 4095
  29. 23rd
  30. 900
  31. 528
  32. 117
  33. 21
  34. 676
  35. 55
  36. 496
  37. 24
  38. 216
  39. 306
  40. 28th

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