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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 295 · 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 the first 5 terms of the AP 6, 12, 18, …? (a) 180 (b) 105 (c) 90 (d) 30
  2. 2.What is the sum of the first 10 terms of the AP 4, 5, 6, …? (a) 13 (b) 170 (c) 85 (d) 90
  3. 3.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 156 (d) 144
  4. 4.What is the 28th term of the AP 19, 28, 37, 46, …? (a) 271 (b) 243 (c) 252 (d) 262
  5. 5.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 100 (c) 55 (d) 19
  6. 6.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 252 (b) 126 (c) 127 (d) 18
  7. 7.What is the 37th term of the AP 18, 25, 32, 39, …? (a) 277 (b) 252 (c) 270 (d) 259
  8. 8.What is the sum of the first 10 terms of the AP 5, 9, 13, …? (a) 41 (b) 230 (c) 250 (d) 460
  9. 9.What is the missing term in the AP 6, 11, ?, 21, 26? (a) 17 (b) 21 (c) 15 (d) 16
  10. 10.What is the sum of the first 12 terms of the AP 9, 13, 17, …? (a) 372 (b) 53 (c) 396 (d) 744
  11. 11.What is the sum of the first 8 terms of the AP 6, 11, 16, …? (a) 208 (b) 41 (c) 188 (d) 376
  12. 12.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 171 (c) 35 (d) 342
  13. 13.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 15 (b) 63 (c) 70 (d) 126
  14. 14.Which term of the AP 12, 20, 28, 36, … is 116? (a) 15th (b) 14th (c) 13th (d) 16th
  15. 15.What is the sum of the first 11 terms of the AP 1, 6, 11, …? (a) 291 (b) 572 (c) 286 (d) 51
  16. 16.What is the 35th term of the AP 15, 21, 27, 33, …? (a) 204 (b) 219 (c) 210 (d) 225
  17. 17.What is the missing term in the AP 19, 24, 29, ?, 39? (a) 35 (b) 34 (c) 33 (d) 39
  18. 18.What is the 10th term of the AP 1, 6, 11, 16, …? (a) 46 (b) 50 (c) 45 (d) 51
  19. 19.What is the sum of all the whole numbers from 1 to 50? (a) 1275 (b) 1250 (c) 2550 (d) 1225
  20. 20.What is the sum of all the whole numbers from 1 to 22? (a) 242 (b) 231 (c) 253 (d) 506
  21. 21.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 930 (c) 59 (d) 900
  22. 22.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 11 (c) 42 (d) 36
  23. 23.What is the sum of all the whole numbers from 1 to 30? (a) 930 (b) 435 (c) 465 (d) 450
  24. 24.What is the 20th term of the AP 4, 9, 14, 19, …? (a) 104 (b) 95 (c) 100 (d) 99
  25. 25.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 380 (c) 37 (d) 190
  26. 26.Which term of the AP 14, 18, 22, 26, … is 106? (a) 26th (b) 24th (c) 25th (d) 23rd
  27. 27.What is the missing term in the AP 4, ?, 16, 22, 28? (a) 16 (b) 10 (c) 11 (d) 9
  28. 28.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 15 (b) 92 (c) 96 (d) 184
  29. 29.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 276 (c) 45 (d) 552
  30. 30.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 108 (b) 54 (c) 14 (d) 60
  31. 31.What is the 12th term of the AP 4, 7, 10, 13, …? (a) 33 (b) 36 (c) 37 (d) 40
  32. 32.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 126 (b) 63 (c) 13 (d) 66
  33. 33.What is the 28th term of the AP 10, 18, 26, 34, …? (a) 226 (b) 224 (c) 234 (d) 216
  34. 34.What is the 36th term of the AP 1, 5, 9, 13, …? (a) 144 (b) 141 (c) 140 (d) 145
  35. 35.What is the 16th term of the AP 6, 8, 10, 12, …? (a) 38 (b) 30 (c) 32 (d) 36
  36. 36.What is the missing term in the AP 2, 6, ?, 14, 18? (a) 11 (b) 10 (c) 9 (d) 14
  37. 37.What is the 26th term of the AP 19, 23, 27, 31, …? (a) 100 (b) 119 (c) 104 (d) 123
  38. 38.What is the 27th term of the AP 15, 23, 31, 39, …? (a) 208 (b) 216 (c) 223 (d) 231
  39. 39.What is the 13th term of the AP 8, 13, 18, 23, …? (a) 65 (b) 60 (c) 68 (d) 73
  40. 40.What is the sum of the first 6 terms of the AP 8, 11, 14, …? (a) 186 (b) 23 (c) 102 (d) 93

Answer key

  1. 90
  2. 85
  3. 144
  4. 262
  5. 100
  6. 126
  7. 270
  8. 230
  9. 16
  10. 372
  11. 188
  12. 324
  13. 63
  14. 14th
  15. 286
  16. 219
  17. 34
  18. 46
  19. 1275
  20. 253
  21. 900
  22. 36
  23. 465
  24. 99
  25. 361
  26. 24th
  27. 10
  28. 92
  29. 529
  30. 54
  31. 37
  32. 63
  33. 226
  34. 141
  35. 36
  36. 10
  37. 119
  38. 223
  39. 68
  40. 93

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