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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 818 · 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.Which term of the AP 10, 14, 18, 22, … is 114? (a) 27th (b) 29th (c) 28th (d) 26th
  2. 2.What is the sum of the first 5 terms of the AP 10, 16, 22, …? (a) 220 (b) 125 (c) 34 (d) 110
  3. 3.Which term of the AP 1, 8, 15, 22, … is 260? (a) 38th (b) 37th (c) 40th (d) 39th
  4. 4.What is the 15th term of the AP 8, 10, 12, 14, …? (a) 38 (b) 28 (c) 30 (d) 36
  5. 5.What is the 31st term of the AP 3, 9, 15, 21, …? (a) 183 (b) 180 (c) 186 (d) 189
  6. 6.What is the 24th term of the AP 10, 18, 26, 34, …? (a) 194 (b) 192 (c) 184 (d) 202
  7. 7.What is the sum of the first 12 terms of the AP 10, 15, 20, …? (a) 900 (b) 480 (c) 65 (d) 450
  8. 8.What is the 33rd term of the AP 3, 5, 7, 9, …? (a) 67 (b) 69 (c) 66 (d) 64
  9. 9.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 380 (c) 37 (d) 361
  10. 10.What is the sum of the first 11 terms of the AP 10, 13, 16, …? (a) 275 (b) 40 (c) 550 (d) 278
  11. 11.What is the sum of the first 10 terms of the AP 7, 13, 19, …? (a) 680 (b) 340 (c) 370 (d) 61
  12. 12.What is the 34th term of the AP 14, 16, 18, 20, …? (a) 66 (b) 82 (c) 68 (d) 80
  13. 13.What is the sum of the first 7 terms of the AP 7, 8, 9, …? (a) 70 (b) 140 (c) 71 (d) 13
  14. 14.What is the 25th term of the AP 12, 15, 18, 21, …? (a) 72 (b) 84 (c) 75 (d) 87
  15. 15.What is the missing term in the AP 6, ?, 24, 33, 42? (a) 16 (b) 24 (c) 15 (d) 14
  16. 16.What is the 10th term of the AP 7, 16, 25, 34, …? (a) 88 (b) 81 (c) 97 (d) 90
  17. 17.What is the sum of all the whole numbers from 1 to 14? (a) 91 (b) 98 (c) 105 (d) 210
  18. 18.What is the 19th term of the AP 7, 12, 17, 22, …? (a) 97 (b) 102 (c) 95 (d) 90
  19. 19.What is the missing term in the AP 2, 7, ?, 17, 22? (a) 12 (b) 11 (c) 13 (d) 17
  20. 20.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 17 (c) 90 (d) 45
  21. 21.Which term of the AP 18, 20, 22, 24, … is 54? (a) 20th (b) 27th (c) 18th (d) 19th
  22. 22.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 49 (c) 56 (d) 28
  23. 23.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 91 (b) 94 (c) 22 (d) 182
  24. 24.What is the sum of the first 9 terms of the AP 5, 8, 11, …? (a) 156 (b) 29 (c) 306 (d) 153
  25. 25.What is the 12th term of the AP 18, 22, 26, 30, …? (a) 48 (b) 44 (c) 66 (d) 62
  26. 26.Which term of the AP 5, 10, 15, 20, … is 100? (a) 22nd (b) 19th (c) 20th (d) 21st
  27. 27.What is the sum of all the whole numbers from 1 to 72? (a) 2592 (b) 5256 (c) 2628 (d) 2556
  28. 28.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 11 (c) 36 (d) 21
  29. 29.What is the sum of all the whole numbers from 1 to 90? (a) 4050 (b) 8190 (c) 4095 (d) 4005
  30. 30.What is the sum of all the whole numbers from 1 to 31? (a) 496 (b) 497 (c) 992 (d) 465
  31. 31.What is the 15th term of the AP 3, 5, 7, 9, …? (a) 30 (b) 28 (c) 33 (d) 31
  32. 32.What is the 33rd term of the AP 5, 7, 9, 11, …? (a) 69 (b) 66 (c) 64 (d) 71
  33. 33.What is the 30th term of the AP 9, 11, 13, 15, …? (a) 60 (b) 58 (c) 69 (d) 67
  34. 34.What is the sum of the first 11 terms of the AP 7, 12, 17, …? (a) 357 (b) 704 (c) 57 (d) 352
  35. 35.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 870 (c) 841 (d) 435
  36. 36.What is the 23rd term of the AP 9, 15, 21, 27, …? (a) 141 (b) 138 (c) 132 (d) 147
  37. 37.Which term of the AP 12, 16, 20, 24, … is 40? (a) 10th (b) 8th (c) 7th (d) 9th
  38. 38.What is the sum of all the whole numbers from 1 to 60? (a) 1770 (b) 1830 (c) 3660 (d) 1800
  39. 39.What is the 33rd term of the AP 14, 23, 32, 41, …? (a) 302 (b) 311 (c) 288 (d) 297
  40. 40.What is the missing term in the AP 7, 13, ?, 25, 31? (a) 18 (b) 20 (c) 19 (d) 25

Answer key

  1. 27th
  2. 110
  3. 38th
  4. 36
  5. 183
  6. 194
  7. 450
  8. 67
  9. 361
  10. 275
  11. 340
  12. 80
  13. 70
  14. 84
  15. 15
  16. 88
  17. 105
  18. 97
  19. 12
  20. 81
  21. 19th
  22. 49
  23. 91
  24. 153
  25. 62
  26. 20th
  27. 2628
  28. 36
  29. 4095
  30. 496
  31. 31
  32. 69
  33. 67
  34. 352
  35. 841
  36. 141
  37. 8th
  38. 1830
  39. 302
  40. 19

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