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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 399 · 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 33rd term of the AP 15, 20, 25, 30, …? (a) 165 (b) 175 (c) 180 (d) 160
  2. 2.What is the 13th term of the AP 2, 6, 10, 14, …? (a) 52 (b) 54 (c) 48 (d) 50
  3. 3.What is the missing term in the AP 6, 8, 10, ?, 14? (a) 11 (b) 13 (c) 14 (d) 12
  4. 4.What is the 14th term of the AP 9, 12, 15, 18, …? (a) 48 (b) 42 (c) 51 (d) 39
  5. 5.What is the missing term in the AP 14, 17, ?, 23, 26? (a) 21 (b) 19 (c) 23 (d) 20
  6. 6.What is the sum of all the whole numbers from 1 to 53? (a) 1432 (b) 2862 (c) 1378 (d) 1431
  7. 7.What is the sum of the first 6 terms of the AP 6, 12, 18, …? (a) 126 (b) 36 (c) 252 (d) 144
  8. 8.What is the 22nd term of the AP 18, 23, 28, 33, …? (a) 105 (b) 110 (c) 128 (d) 123
  9. 9.Which term of the AP 11, 16, 21, 26, … is 156? (a) 29th (b) 30th (c) 31st (d) 32nd
  10. 10.What is the sum of all the whole numbers from 1 to 72? (a) 2556 (b) 2592 (c) 5256 (d) 2628
  11. 11.What is the 38th term of the AP 16, 24, 32, 40, …? (a) 312 (b) 320 (c) 304 (d) 296
  12. 12.What is the missing term in the AP 4, ?, 22, 31, 40? (a) 14 (b) 12 (c) 22 (d) 13
  13. 13.What is the 12th term of the AP 6, 10, 14, 18, …? (a) 48 (b) 54 (c) 44 (d) 50
  14. 14.Which term of the AP 8, 12, 16, 20, … is 76? (a) 19th (b) 20th (c) 17th (d) 18th
  15. 15.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 63 (b) 56 (c) 14 (d) 112
  16. 16.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 756 (d) 729
  17. 17.What is the sum of all the whole numbers from 1 to 81? (a) 3321 (b) 3322 (c) 3240 (d) 6642
  18. 18.Which term of the AP 18, 20, 22, 24, … is 80? (a) 32nd (b) 31st (c) 40th (d) 33rd
  19. 19.Which term of the AP 1, 10, 19, 28, … is 289? (a) 35th (b) 34th (c) 33rd (d) 32nd
  20. 20.What is the missing term in the AP 19, 26, 33, ?, 47? (a) 40 (b) 41 (c) 47 (d) 39
  21. 21.What is the 31st term of the AP 3, 12, 21, 30, …? (a) 282 (b) 273 (c) 270 (d) 279
  22. 22.What is the sum of the first 10 terms of the AP 1, 5, 9, …? (a) 380 (b) 37 (c) 210 (d) 190
  23. 23.What is the 24th term of the AP 16, 24, 32, 40, …? (a) 184 (b) 192 (c) 208 (d) 200
  24. 24.What is the sum of all the whole numbers from 1 to 58? (a) 3422 (b) 1711 (c) 1653 (d) 1682
  25. 25.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 84 (b) 19 (c) 168 (d) 90
  26. 26.What is the 22nd term of the AP 5, 10, 15, 20, …? (a) 105 (b) 115 (c) 111 (d) 110
  27. 27.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 231 (c) 41 (d) 462
  28. 28.What is the sum of all the whole numbers from 1 to 24? (a) 300 (b) 600 (c) 288 (d) 276
  29. 29.What is the missing term in the AP 16, 25, 34, ?, 52? (a) 42 (b) 52 (c) 43 (d) 44
  30. 30.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 870 (c) 841 (d) 57
  31. 31.Which term of the AP 14, 19, 24, 29, … is 69? (a) 11th (b) 12th (c) 13th (d) 14th
  32. 32.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 256 (b) 38 (c) 506 (d) 253
  33. 33.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 21 (d) 121
  34. 34.What is the sum of the first 12 terms of the AP 6, 11, 16, …? (a) 804 (b) 402 (c) 432 (d) 61
  35. 35.Which term of the AP 14, 16, 18, 20, … is 84? (a) 37th (b) 42nd (c) 35th (d) 36th
  36. 36.What is the 17th term of the AP 1, 5, 9, 13, …? (a) 69 (b) 65 (c) 64 (d) 68
  37. 37.What is the sum of the first 11 terms of the AP 9, 10, 11, …? (a) 308 (b) 154 (c) 155 (d) 19
  38. 38.What is the sum of all the whole numbers from 1 to 39? (a) 780 (b) 741 (c) 781 (d) 1560
  39. 39.What is the sum of all the whole numbers from 1 to 11? (a) 132 (b) 55 (c) 66 (d) 67
  40. 40.What is the 14th term of the AP 1, 5, 9, 13, …? (a) 53 (b) 52 (c) 56 (d) 57

Answer key

  1. 175
  2. 50
  3. 12
  4. 48
  5. 20
  6. 1431
  7. 126
  8. 123
  9. 30th
  10. 2628
  11. 312
  12. 13
  13. 50
  14. 18th
  15. 56
  16. 729
  17. 3321
  18. 32nd
  19. 33rd
  20. 40
  21. 273
  22. 190
  23. 200
  24. 1711
  25. 84
  26. 110
  27. 441
  28. 300
  29. 43
  30. 841
  31. 12th
  32. 253
  33. 121
  34. 402
  35. 36th
  36. 65
  37. 154
  38. 780
  39. 66
  40. 53

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