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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 761 · 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 82? (a) 3321 (b) 6806 (c) 3403 (d) 3362
  2. 2.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 7 (b) 54 (c) 30 (d) 27
  3. 3.What is the missing term in the AP 19, 24, 29, ?, 39? (a) 34 (b) 35 (c) 39 (d) 33
  4. 4.What is the 39th term of the AP 7, 16, 25, 34, …? (a) 349 (b) 351 (c) 342 (d) 358
  5. 5.What is the missing term in the AP 10, 15, 20, ?, 30? (a) 30 (b) 24 (c) 26 (d) 25
  6. 6.What is the missing term in the AP 15, 24, ?, 42, 51? (a) 32 (b) 42 (c) 33 (d) 34
  7. 7.What is the 22nd term of the AP 8, 15, 22, 29, …? (a) 155 (b) 147 (c) 154 (d) 162
  8. 8.What is the 26th term of the AP 3, 6, 9, 12, …? (a) 79 (b) 75 (c) 81 (d) 78
  9. 9.What is the sum of the first 12 terms of the AP 4, 5, 6, …? (a) 114 (b) 15 (c) 120 (d) 228
  10. 10.What is the 15th term of the AP 1, 6, 11, 16, …? (a) 71 (b) 76 (c) 70 (d) 75
  11. 11.What is the 19th term of the AP 3, 12, 21, 30, …? (a) 174 (b) 171 (c) 162 (d) 165
  12. 12.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 56 (c) 28 (d) 49
  13. 13.What is the 40th term of the AP 4, 11, 18, 25, …? (a) 280 (b) 284 (c) 273 (d) 277
  14. 14.What is the 34th term of the AP 15, 24, 33, 42, …? (a) 306 (b) 321 (c) 312 (d) 297
  15. 15.What is the 30th term of the AP 16, 22, 28, 34, …? (a) 180 (b) 190 (c) 196 (d) 174
  16. 16.What is the sum of all the whole numbers from 1 to 92? (a) 4232 (b) 4278 (c) 8556 (d) 4186
  17. 17.What is the sum of all the whole numbers from 1 to 70? (a) 2485 (b) 4970 (c) 2450 (d) 2415
  18. 18.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 7 (b) 5 (c) 4 (d) 3
  19. 19.What is the 21st term of the AP 2, 5, 8, 11, …? (a) 62 (b) 63 (c) 60 (d) 65
  20. 20.What is the missing term in the AP 9, ?, 17, 21, 25? (a) 13 (b) 17 (c) 12 (d) 14
  21. 21.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 27 (b) 270 (c) 138 (d) 135
  22. 22.What is the sum of the first 6 terms of the AP 9, 14, 19, …? (a) 144 (b) 129 (c) 34 (d) 258
  23. 23.What is the 17th term of the AP 15, 20, 25, 30, …? (a) 95 (b) 80 (c) 85 (d) 100
  24. 24.What is the 37th term of the AP 17, 21, 25, 29, …? (a) 165 (b) 148 (c) 144 (d) 161
  25. 25.Which term of the AP 2, 6, 10, 14, … is 58? (a) 15th (b) 16th (c) 14th (d) 17th
  26. 26.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 42 (c) 11 (d) 21
  27. 27.Which term of the AP 19, 25, 31, 37, … is 79? (a) 12th (b) 10th (c) 13th (d) 11th
  28. 28.What is the sum of all the whole numbers from 1 to 16? (a) 272 (b) 120 (c) 136 (d) 128
  29. 29.What is the 14th term of the AP 2, 4, 6, 8, …? (a) 30 (b) 26 (c) 29 (d) 28
  30. 30.What is the sum of all the whole numbers from 1 to 100? (a) 5050 (b) 5000 (c) 10100 (d) 4950
  31. 31.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 43 (c) 484 (d) 253
  32. 32.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 100 (c) 110 (d) 19
  33. 33.What is the sum of the first 8 terms of the AP 10, 16, 22, …? (a) 52 (b) 496 (c) 248 (d) 272
  34. 34.Which term of the AP 3, 6, 9, 12, … is 45? (a) 14th (b) 17th (c) 16th (d) 15th
  35. 35.What is the missing term in the AP 12, ?, 18, 21, 24? (a) 16 (b) 15 (c) 14 (d) 18
  36. 36.What is the sum of the first 7 terms of the AP 10, 14, 18, …? (a) 34 (b) 308 (c) 168 (d) 154
  37. 37.Which term of the AP 3, 9, 15, 21, … is 153? (a) 25th (b) 26th (c) 27th (d) 28th
  38. 38.What is the sum of the first 7 terms of the AP 7, 13, 19, …? (a) 175 (b) 350 (c) 196 (d) 43
  39. 39.What is the sum of the first 12 terms of the AP 2, 6, 10, …? (a) 312 (b) 288 (c) 46 (d) 576
  40. 40.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 30 (b) 228 (c) 456 (d) 240

Answer key

  1. 3403
  2. 27
  3. 34
  4. 349
  5. 25
  6. 33
  7. 155
  8. 78
  9. 114
  10. 71
  11. 165
  12. 49
  13. 277
  14. 312
  15. 190
  16. 4278
  17. 2485
  18. 4
  19. 62
  20. 13
  21. 135
  22. 129
  23. 95
  24. 161
  25. 15th
  26. 36
  27. 11th
  28. 136
  29. 28
  30. 5050
  31. 484
  32. 100
  33. 248
  34. 15th
  35. 15
  36. 154
  37. 26th
  38. 175
  39. 288
  40. 228

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