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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 815 · 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 all the whole numbers from 1 to 39? (a) 780 (b) 781 (c) 741 (d) 1560
  2. 2.What is the missing term in the AP 16, ?, 34, 43, 52? (a) 25 (b) 26 (c) 34 (d) 24
  3. 3.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 126 (b) 18 (c) 252 (d) 127
  4. 4.What is the sum of the first 6 terms of the AP 4, 7, 10, …? (a) 19 (b) 69 (c) 138 (d) 78
  5. 5.What is the 40th term of the AP 19, 27, 35, 43, …? (a) 320 (b) 339 (c) 331 (d) 312
  6. 6.What is the missing term in the AP 4, 8, 12, ?, 20? (a) 20 (b) 17 (c) 16 (d) 15
  7. 7.What is the missing term in the AP 15, ?, 23, 27, 31? (a) 20 (b) 23 (c) 18 (d) 19
  8. 8.What is the 27th term of the AP 3, 12, 21, 30, …? (a) 237 (b) 246 (c) 243 (d) 234
  9. 9.What is the 29th term of the AP 9, 17, 25, 33, …? (a) 232 (b) 224 (c) 241 (d) 233
  10. 10.What is the sum of the first 11 terms of the AP 2, 6, 10, …? (a) 42 (b) 242 (c) 484 (d) 264
  11. 11.What is the 16th term of the AP 10, 19, 28, 37, …? (a) 144 (b) 154 (c) 145 (d) 135
  12. 12.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 400 (c) 39 (d) 420
  13. 13.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 29 (b) 216 (c) 432 (d) 228
  14. 14.What is the sum of the first 10 terms of the AP 5, 6, 7, …? (a) 190 (b) 100 (c) 95 (d) 14
  15. 15.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 414 (b) 828 (c) 444 (d) 62
  16. 16.Which term of the AP 9, 13, 17, 21, … is 137? (a) 35th (b) 33rd (c) 32nd (d) 34th
  17. 17.What is the 38th term of the AP 11, 13, 15, 17, …? (a) 74 (b) 76 (c) 87 (d) 85
  18. 18.What is the 16th term of the AP 3, 12, 21, 30, …? (a) 147 (b) 144 (c) 135 (d) 138
  19. 19.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 462 (c) 41 (d) 231
  20. 20.What is the 18th term of the AP 2, 4, 6, 8, …? (a) 34 (b) 36 (c) 37 (d) 38
  21. 21.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 11 (b) 51 (c) 102 (d) 54
  22. 22.What is the 18th term of the AP 16, 18, 20, 22, …? (a) 52 (b) 50 (c) 34 (d) 36
  23. 23.What is the sum of the first 8 terms of the AP 6, 7, 8, …? (a) 80 (b) 76 (c) 152 (d) 13
  24. 24.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 306 (b) 153 (c) 33 (d) 171
  25. 25.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 384 (b) 45 (c) 216 (d) 192
  26. 26.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 52 (b) 302 (c) 594 (d) 297
  27. 27.What is the sum of the first 8 terms of the AP 9, 13, 17, …? (a) 368 (b) 37 (c) 200 (d) 184
  28. 28.What is the 15th term of the AP 14, 19, 24, 29, …? (a) 75 (b) 70 (c) 89 (d) 84
  29. 29.What is the 14th term of the AP 6, 13, 20, 27, …? (a) 98 (b) 91 (c) 97 (d) 104
  30. 30.What is the 14th term of the AP 16, 18, 20, 22, …? (a) 44 (b) 42 (c) 26 (d) 28
  31. 31.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 126 (b) 111 (c) 222 (d) 31
  32. 32.What is the sum of all the whole numbers from 1 to 56? (a) 1568 (b) 3192 (c) 1540 (d) 1596
  33. 33.What is the missing term in the AP 5, 7, ?, 11, 13? (a) 11 (b) 9 (c) 8 (d) 10
  34. 34.What is the 15th term of the AP 11, 16, 21, 26, …? (a) 75 (b) 86 (c) 70 (d) 81
  35. 35.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 351 (c) 676 (d) 51
  36. 36.What is the missing term in the AP 16, 22, 28, ?, 40? (a) 35 (b) 40 (c) 33 (d) 34
  37. 37.What is the missing term in the AP 13, 18, ?, 28, 33? (a) 28 (b) 22 (c) 23 (d) 24
  38. 38.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 72 (b) 14 (c) 69 (d) 138
  39. 39.What is the missing term in the AP 11, 20, 29, ?, 47? (a) 37 (b) 47 (c) 38 (d) 39
  40. 40.What is the 30th term of the AP 8, 17, 26, 35, …? (a) 269 (b) 270 (c) 278 (d) 261

Answer key

  1. 780
  2. 25
  3. 126
  4. 69
  5. 331
  6. 16
  7. 19
  8. 237
  9. 233
  10. 242
  11. 145
  12. 400
  13. 216
  14. 95
  15. 414
  16. 33rd
  17. 85
  18. 138
  19. 441
  20. 36
  21. 51
  22. 50
  23. 76
  24. 153
  25. 192
  26. 297
  27. 184
  28. 84
  29. 97
  30. 42
  31. 111
  32. 1596
  33. 9
  34. 81
  35. 676
  36. 34
  37. 23
  38. 69
  39. 38
  40. 269

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