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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 507 · 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 71? (a) 2485 (b) 2557 (c) 5112 (d) 2556
  2. 2.What is the sum of the first 8 terms of the AP 8, 14, 20, …? (a) 256 (b) 464 (c) 232 (d) 50
  3. 3.What is the 15th term of the AP 5, 14, 23, 32, …? (a) 135 (b) 140 (c) 131 (d) 126
  4. 4.What is the 33rd term of the AP 16, 20, 24, 28, …? (a) 144 (b) 148 (c) 128 (d) 132
  5. 5.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 65 (b) 70 (c) 17 (d) 130
  6. 6.What is the 31st term of the AP 5, 12, 19, 26, …? (a) 210 (b) 222 (c) 215 (d) 217
  7. 7.What is the sum of all the whole numbers from 1 to 93? (a) 4371 (b) 4278 (c) 4372 (d) 8742
  8. 8.What is the 34th term of the AP 12, 18, 24, 30, …? (a) 198 (b) 210 (c) 216 (d) 204
  9. 9.What is the sum of the first 9 terms of the AP 6, 12, 18, …? (a) 54 (b) 297 (c) 540 (d) 270
  10. 10.Which term of the AP 12, 16, 20, 24, … is 96? (a) 24th (b) 21st (c) 23rd (d) 22nd
  11. 11.What is the sum of all the whole numbers from 1 to 56? (a) 3192 (b) 1596 (c) 1540 (d) 1568
  12. 12.Which term of the AP 11, 17, 23, 29, … is 125? (a) 21st (b) 20th (c) 22nd (d) 19th
  13. 13.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 320 (b) 580 (c) 56 (d) 290
  14. 14.What is the missing term in the AP 7, 11, 15, ?, 23? (a) 19 (b) 20 (c) 23 (d) 18
  15. 15.What is the sum of all the whole numbers from 1 to 55? (a) 3080 (b) 1485 (c) 1541 (d) 1540
  16. 16.What is the 22nd term of the AP 1, 4, 7, 10, …? (a) 66 (b) 63 (c) 64 (d) 67
  17. 17.Which term of the AP 17, 21, 25, 29, … is 125? (a) 30th (b) 29th (c) 27th (d) 28th
  18. 18.What is the 15th term of the AP 11, 20, 29, 38, …? (a) 137 (b) 126 (c) 146 (d) 135
  19. 19.What is the 12th term of the AP 8, 11, 14, 17, …? (a) 36 (b) 44 (c) 33 (d) 41
  20. 20.Which term of the AP 3, 8, 13, 18, … is 43? (a) 9th (b) 10th (c) 11th (d) 8th
  21. 21.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 36 (b) 35 (c) 70 (d) 8
  22. 22.What is the sum of all the whole numbers from 1 to 70? (a) 4970 (b) 2450 (c) 2485 (d) 2415
  23. 23.Which term of the AP 4, 10, 16, 22, … is 136? (a) 22nd (b) 24th (c) 25th (d) 23rd
  24. 24.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 90 (b) 11 (c) 46 (d) 45
  25. 25.What is the 15th term of the AP 20, 26, 32, 38, …? (a) 110 (b) 104 (c) 84 (d) 90
  26. 26.What is the 37th term of the AP 10, 17, 24, 31, …? (a) 259 (b) 269 (c) 252 (d) 262
  27. 27.What is the missing term in the AP 4, 11, ?, 25, 32? (a) 18 (b) 19 (c) 17 (d) 25
  28. 28.What is the 15th term of the AP 19, 24, 29, 34, …? (a) 75 (b) 94 (c) 89 (d) 70
  29. 29.What is the 39th term of the AP 9, 12, 15, 18, …? (a) 117 (b) 114 (c) 126 (d) 123
  30. 30.What is the missing term in the AP 12, 17, ?, 27, 32? (a) 27 (b) 21 (c) 23 (d) 22
  31. 31.What is the sum of all the whole numbers from 1 to 96? (a) 4656 (b) 9312 (c) 4608 (d) 4560
  32. 32.What is the 13th term of the AP 1, 7, 13, 19, …? (a) 79 (b) 73 (c) 72 (d) 78
  33. 33.What is the 19th term of the AP 9, 13, 17, 21, …? (a) 72 (b) 76 (c) 81 (d) 85
  34. 34.What is the sum of the first 10 terms of the AP 6, 9, 12, …? (a) 195 (b) 390 (c) 33 (d) 210
  35. 35.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 41 (c) 231 (d) 462
  36. 36.What is the sum of all the whole numbers from 1 to 59? (a) 1711 (b) 3540 (c) 1770 (d) 1771
  37. 37.What is the sum of all the whole numbers from 1 to 20? (a) 200 (b) 190 (c) 420 (d) 210
  38. 38.Which term of the AP 13, 19, 25, 31, … is 199? (a) 33rd (b) 31st (c) 32nd (d) 34th
  39. 39.Which term of the AP 7, 9, 11, 13, … is 23? (a) 8th (b) 9th (c) 11th (d) 10th
  40. 40.Which term of the AP 2, 5, 8, 11, … is 38? (a) 12th (b) 15th (c) 14th (d) 13th

Answer key

  1. 2556
  2. 232
  3. 131
  4. 144
  5. 65
  6. 215
  7. 4371
  8. 210
  9. 270
  10. 22nd
  11. 1596
  12. 20th
  13. 290
  14. 19
  15. 1540
  16. 64
  17. 28th
  18. 137
  19. 41
  20. 9th
  21. 35
  22. 2485
  23. 23rd
  24. 45
  25. 104
  26. 262
  27. 18
  28. 89
  29. 123
  30. 22
  31. 4656
  32. 73
  33. 81
  34. 195
  35. 441
  36. 1770
  37. 210
  38. 32nd
  39. 9th
  40. 13th

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