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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 349 · 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 24th term of the AP 13, 21, 29, 37, …? (a) 192 (b) 197 (c) 205 (d) 184
  2. 2.What is the missing term in the AP 6, 15, 24, ?, 42? (a) 42 (b) 34 (c) 32 (d) 33
  3. 3.What is the 36th term of the AP 4, 11, 18, 25, …? (a) 245 (b) 252 (c) 249 (d) 256
  4. 4.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 242 (b) 121 (c) 132 (d) 21
  5. 5.What is the 37th term of the AP 9, 16, 23, 30, …? (a) 259 (b) 268 (c) 261 (d) 252
  6. 6.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 25 (b) 65 (c) 130 (d) 80
  7. 7.What is the sum of the first 9 terms of the AP 10, 16, 22, …? (a) 58 (b) 612 (c) 306 (d) 333
  8. 8.What is the 31st term of the AP 19, 22, 25, 28, …? (a) 93 (b) 90 (c) 109 (d) 112
  9. 9.What is the sum of the first 10 terms of the AP 6, 11, 16, …? (a) 310 (b) 570 (c) 285 (d) 51
  10. 10.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 136 (c) 272 (d) 256
  11. 11.What is the 16th term of the AP 20, 23, 26, 29, …? (a) 48 (b) 68 (c) 45 (d) 65
  12. 12.What is the sum of the first 10 terms of the AP 5, 6, 7, …? (a) 190 (b) 100 (c) 95 (d) 14
  13. 13.What is the 39th term of the AP 4, 6, 8, 10, …? (a) 78 (b) 82 (c) 80 (d) 76
  14. 14.What is the missing term in the AP 12, ?, 28, 36, 44? (a) 19 (b) 20 (c) 28 (d) 21
  15. 15.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 43 (c) 253 (d) 506
  16. 16.What is the sum of the first 11 terms of the AP 1, 5, 9, …? (a) 253 (b) 41 (c) 231 (d) 462
  17. 17.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 480 (b) 240 (c) 31 (d) 252
  18. 18.What is the 14th term of the AP 11, 18, 25, 32, …? (a) 98 (b) 91 (c) 109 (d) 102
  19. 19.Which term of the AP 17, 20, 23, 26, … is 53? (a) 13th (b) 12th (c) 15th (d) 14th
  20. 20.What is the 40th term of the AP 11, 15, 19, 23, …? (a) 167 (b) 156 (c) 160 (d) 171
  21. 21.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 91 (c) 25 (d) 169
  22. 22.Which term of the AP 7, 12, 17, 22, … is 97? (a) 18th (b) 19th (c) 21st (d) 20th
  23. 23.What is the 20th term of the AP 20, 27, 34, 41, …? (a) 140 (b) 153 (c) 160 (d) 133
  24. 24.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 43 (b) 9 (c) 84 (d) 42
  25. 25.Which term of the AP 8, 17, 26, 35, … is 332? (a) 39th (b) 37th (c) 36th (d) 38th
  26. 26.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 35 (b) 240 (c) 138 (d) 120
  27. 27.What is the 40th term of the AP 14, 19, 24, 29, …? (a) 200 (b) 214 (c) 195 (d) 209
  28. 28.What is the sum of all the whole numbers from 1 to 96? (a) 9312 (b) 4560 (c) 4608 (d) 4656
  29. 29.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 98 (b) 49 (c) 56 (d) 13
  30. 30.What is the missing term in the AP 14, ?, 22, 26, 30? (a) 18 (b) 19 (c) 17 (d) 22
  31. 31.What is the missing term in the AP 12, ?, 30, 39, 48? (a) 21 (b) 22 (c) 30 (d) 20
  32. 32.What is the sum of all the whole numbers from 1 to 78? (a) 3003 (b) 6162 (c) 3042 (d) 3081
  33. 33.What is the 14th term of the AP 16, 21, 26, 31, …? (a) 81 (b) 65 (c) 86 (d) 70
  34. 34.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 57 (b) 708 (c) 384 (d) 354
  35. 35.Which term of the AP 10, 17, 24, 31, … is 66? (a) 8th (b) 10th (c) 9th (d) 11th
  36. 36.What is the sum of the first 7 terms of the AP 6, 7, 8, …? (a) 12 (b) 64 (c) 63 (d) 126
  37. 37.What is the sum of the first 10 terms of the AP 9, 15, 21, …? (a) 63 (b) 720 (c) 360 (d) 390
  38. 38.What is the missing term in the AP 13, 16, ?, 22, 25? (a) 19 (b) 18 (c) 22 (d) 20
  39. 39.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 300 (c) 47 (d) 576
  40. 40.What is the 23rd term of the AP 5, 10, 15, 20, …? (a) 116 (b) 120 (c) 110 (d) 115

Answer key

  1. 197
  2. 33
  3. 249
  4. 121
  5. 261
  6. 65
  7. 306
  8. 109
  9. 285
  10. 256
  11. 65
  12. 95
  13. 80
  14. 20
  15. 484
  16. 231
  17. 240
  18. 102
  19. 13th
  20. 167
  21. 169
  22. 19th
  23. 153
  24. 42
  25. 37th
  26. 120
  27. 209
  28. 4656
  29. 49
  30. 18
  31. 21
  32. 3081
  33. 81
  34. 354
  35. 9th
  36. 63
  37. 360
  38. 19
  39. 576
  40. 115

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