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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 409 · 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 missing term in the AP 5, 10, ?, 20, 25? (a) 14 (b) 15 (c) 20 (d) 16
  2. 2.What is the 27th term of the AP 12, 20, 28, 36, …? (a) 216 (b) 228 (c) 220 (d) 208
  3. 3.What is the sum of the first 10 terms of the AP 9, 14, 19, …? (a) 54 (b) 315 (c) 340 (d) 630
  4. 4.What is the 30th term of the AP 12, 18, 24, 30, …? (a) 186 (b) 174 (c) 180 (d) 192
  5. 5.Which term of the AP 19, 25, 31, 37, … is 67? (a) 9th (b) 10th (c) 8th (d) 11th
  6. 6.Which term of the AP 16, 19, 22, 25, … is 49? (a) 13th (b) 11th (c) 14th (d) 12th
  7. 7.What is the sum of all the whole numbers from 1 to 52? (a) 2756 (b) 1378 (c) 1352 (d) 1326
  8. 8.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 20 (b) 154 (c) 77 (d) 80
  9. 9.What is the 37th term of the AP 6, 14, 22, 30, …? (a) 296 (b) 302 (c) 288 (d) 294
  10. 10.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 39 (b) 9 (c) 42 (d) 78
  11. 11.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 49 (c) 28 (d) 13
  12. 12.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 44 (b) 203 (c) 182 (d) 364
  13. 13.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 15 (b) 85 (c) 168 (d) 84
  14. 14.What is the sum of the first 6 terms of the AP 6, 9, 12, …? (a) 21 (b) 90 (c) 162 (d) 81
  15. 15.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 45 (c) 529 (d) 276
  16. 16.What is the missing term in the AP 9, 12, ?, 18, 21? (a) 14 (b) 18 (c) 15 (d) 16
  17. 17.Which term of the AP 2, 5, 8, 11, … is 107? (a) 35th (b) 37th (c) 38th (d) 36th
  18. 18.What is the missing term in the AP 4, 7, 10, ?, 16? (a) 13 (b) 16 (c) 14 (d) 12
  19. 19.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 64 (c) 72 (d) 15
  20. 20.What is the sum of all the whole numbers from 1 to 40? (a) 780 (b) 820 (c) 1640 (d) 800
  21. 21.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 352 (b) 200 (c) 43 (d) 176
  22. 22.What is the missing term in the AP 10, 14, ?, 22, 26? (a) 17 (b) 19 (c) 22 (d) 18
  23. 23.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 289 (c) 306 (d) 33
  24. 24.What is the sum of the first 11 terms of the AP 1, 4, 7, …? (a) 31 (b) 176 (c) 179 (d) 352
  25. 25.What is the 12th term of the AP 14, 18, 22, 26, …? (a) 58 (b) 48 (c) 44 (d) 62
  26. 26.What is the missing term in the AP 5, 9, ?, 17, 21? (a) 13 (b) 17 (c) 12 (d) 14
  27. 27.Which term of the AP 10, 18, 26, 34, … is 170? (a) 22nd (b) 20th (c) 21st (d) 23rd
  28. 28.Which term of the AP 11, 13, 15, 17, … is 81? (a) 37th (b) 38th (c) 36th (d) 35th
  29. 29.What is the 15th term of the AP 8, 16, 24, 32, …? (a) 121 (b) 112 (c) 120 (d) 128
  30. 30.What is the sum of the first 11 terms of the AP 1, 6, 11, …? (a) 291 (b) 572 (c) 286 (d) 51
  31. 31.What is the sum of all the whole numbers from 1 to 27? (a) 756 (b) 351 (c) 379 (d) 378
  32. 32.What is the sum of all the whole numbers from 1 to 55? (a) 3080 (b) 1541 (c) 1540 (d) 1485
  33. 33.What is the 21st term of the AP 16, 25, 34, 43, …? (a) 180 (b) 189 (c) 196 (d) 205
  34. 34.What is the sum of the first 9 terms of the AP 9, 15, 21, …? (a) 57 (b) 324 (c) 297 (d) 594
  35. 35.What is the 33rd term of the AP 12, 18, 24, 30, …? (a) 198 (b) 210 (c) 192 (d) 204
  36. 36.Which term of the AP 14, 21, 28, 35, … is 259? (a) 36th (b) 38th (c) 37th (d) 35th
  37. 37.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 22 (b) 135 (c) 126 (d) 252
  38. 38.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 39 (c) 400 (d) 420
  39. 39.What is the missing term in the AP 8, 17, 26, ?, 44? (a) 36 (b) 44 (c) 35 (d) 34
  40. 40.Which term of the AP 8, 17, 26, 35, … is 152? (a) 16th (b) 18th (c) 17th (d) 19th

Answer key

  1. 15
  2. 220
  3. 315
  4. 186
  5. 9th
  6. 12th
  7. 1378
  8. 77
  9. 294
  10. 39
  11. 49
  12. 182
  13. 84
  14. 81
  15. 529
  16. 15
  17. 36th
  18. 13
  19. 64
  20. 820
  21. 176
  22. 18
  23. 289
  24. 176
  25. 58
  26. 13
  27. 21st
  28. 36th
  29. 120
  30. 286
  31. 378
  32. 1540
  33. 196
  34. 297
  35. 204
  36. 36th
  37. 126
  38. 400
  39. 35
  40. 17th

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