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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 134 · 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, 2, 3, …? (a) 42 (b) 6 (c) 24 (d) 21
  2. 2.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 324 (b) 600 (c) 300 (d) 47
  3. 3.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 540 (b) 75 (c) 1008 (d) 504
  4. 4.What is the sum of the first 10 terms of the AP 3, 5, 7, …? (a) 240 (b) 130 (c) 21 (d) 120
  5. 5.What is the 39th term of the AP 11, 20, 29, 38, …? (a) 362 (b) 351 (c) 342 (d) 353
  6. 6.What is the sum of all the whole numbers from 1 to 80? (a) 6480 (b) 3200 (c) 3160 (d) 3240
  7. 7.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 17 (b) 234 (c) 117 (d) 118
  8. 8.What is the 15th term of the AP 8, 16, 24, 32, …? (a) 112 (b) 120 (c) 121 (d) 128
  9. 9.What is the 37th term of the AP 1, 9, 17, 25, …? (a) 288 (b) 297 (c) 296 (d) 289
  10. 10.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 56 (c) 28 (d) 49
  11. 11.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 33 (b) 36 (c) 66 (d) 8
  12. 12.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 354 (b) 384 (c) 57 (d) 708
  13. 13.Which term of the AP 10, 12, 14, 16, … is 74? (a) 32nd (b) 34th (c) 37th (d) 33rd
  14. 14.What is the sum of the first 10 terms of the AP 10, 11, 12, …? (a) 19 (b) 290 (c) 145 (d) 150
  15. 15.What is the 40th term of the AP 4, 11, 18, 25, …? (a) 284 (b) 280 (c) 277 (d) 273
  16. 16.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 253 (c) 484 (d) 506
  17. 17.What is the missing term in the AP 10, 16, 22, ?, 34? (a) 34 (b) 27 (c) 28 (d) 29
  18. 18.What is the 37th term of the AP 14, 20, 26, 32, …? (a) 222 (b) 236 (c) 230 (d) 216
  19. 19.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 36 (c) 72 (d) 64
  20. 20.What is the 31st term of the AP 10, 12, 14, 16, …? (a) 62 (b) 72 (c) 70 (d) 60
  21. 21.Which term of the AP 6, 11, 16, 21, … is 66? (a) 13th (b) 14th (c) 15th (d) 12th
  22. 22.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 39 (c) 210 (d) 420
  23. 23.What is the sum of the first 9 terms of the AP 10, 15, 20, …? (a) 270 (b) 540 (c) 50 (d) 275
  24. 24.What is the sum of all the whole numbers from 1 to 56? (a) 1568 (b) 1540 (c) 1596 (d) 3192
  25. 25.What is the sum of all the whole numbers from 1 to 59? (a) 1771 (b) 1770 (c) 1711 (d) 3540
  26. 26.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 58 (b) 17 (c) 55 (d) 110
  27. 27.What is the sum of all the whole numbers from 1 to 20? (a) 210 (b) 190 (c) 420 (d) 200
  28. 28.What is the 38th term of the AP 7, 11, 15, 19, …? (a) 148 (b) 152 (c) 155 (d) 159
  29. 29.What is the missing term in the AP 5, ?, 9, 11, 13? (a) 8 (b) 6 (c) 9 (d) 7
  30. 30.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 19 (b) 200 (c) 110 (d) 100
  31. 31.What is the 19th term of the AP 9, 11, 13, 15, …? (a) 47 (b) 36 (c) 38 (d) 45
  32. 32.What is the 23rd term of the AP 17, 19, 21, 23, …? (a) 63 (b) 44 (c) 46 (d) 61
  33. 33.What is the missing term in the AP 9, 12, ?, 18, 21? (a) 16 (b) 14 (c) 18 (d) 15
  34. 34.What is the 35th term of the AP 3, 7, 11, 15, …? (a) 143 (b) 139 (c) 140 (d) 136
  35. 35.What is the sum of all the whole numbers from 1 to 61? (a) 1892 (b) 3782 (c) 1830 (d) 1891
  36. 36.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 26 (b) 180 (c) 170 (d) 340
  37. 37.What is the 20th term of the AP 4, 7, 10, 13, …? (a) 57 (b) 60 (c) 64 (d) 61
  38. 38.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 55 (c) 784 (d) 406
  39. 39.What is the 39th term of the AP 14, 18, 22, 26, …? (a) 152 (b) 170 (c) 156 (d) 166
  40. 40.Which term of the AP 14, 17, 20, 23, … is 92? (a) 26th (b) 29th (c) 28th (d) 27th

Answer key

  1. 21
  2. 300
  3. 504
  4. 120
  5. 353
  6. 3240
  7. 117
  8. 120
  9. 289
  10. 49
  11. 33
  12. 354
  13. 33rd
  14. 145
  15. 277
  16. 484
  17. 28
  18. 230
  19. 64
  20. 70
  21. 13th
  22. 400
  23. 270
  24. 1596
  25. 1770
  26. 55
  27. 210
  28. 155
  29. 7
  30. 100
  31. 45
  32. 61
  33. 15
  34. 139
  35. 1891
  36. 170
  37. 61
  38. 784
  39. 166
  40. 27th

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