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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 482 · 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 67? (a) 2211 (b) 4556 (c) 2278 (d) 2279
  2. 2.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 122 (b) 16 (c) 121 (d) 242
  3. 3.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 374 (b) 187 (c) 198 (d) 27
  4. 4.What is the 15th term of the AP 11, 13, 15, 17, …? (a) 41 (b) 28 (c) 30 (d) 39
  5. 5.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 56 (c) 13 (d) 49
  6. 6.What is the 28th term of the AP 4, 13, 22, 31, …? (a) 247 (b) 252 (c) 256 (d) 243
  7. 7.What is the missing term in the AP 13, ?, 17, 19, 21? (a) 15 (b) 17 (c) 14 (d) 16
  8. 8.What is the sum of the first 9 terms of the AP 6, 12, 18, …? (a) 540 (b) 270 (c) 297 (d) 54
  9. 9.What is the 25th term of the AP 2, 11, 20, 29, …? (a) 227 (b) 216 (c) 218 (d) 225
  10. 10.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 960 (b) 516 (c) 480 (d) 73
  11. 11.What is the 20th term of the AP 19, 27, 35, 43, …? (a) 179 (b) 171 (c) 160 (d) 152
  12. 12.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 19 (c) 100 (d) 110
  13. 13.What is the sum of all the whole numbers from 1 to 10? (a) 55 (b) 45 (c) 50 (d) 110
  14. 14.What is the 34th term of the AP 4, 11, 18, 25, …? (a) 238 (b) 235 (c) 242 (d) 231
  15. 15.What is the 18th term of the AP 15, 18, 21, 24, …? (a) 54 (b) 69 (c) 66 (d) 51
  16. 16.What is the 22nd term of the AP 1, 10, 19, 28, …? (a) 189 (b) 199 (c) 190 (d) 198
  17. 17.What is the missing term in the AP 13, ?, 19, 22, 25? (a) 19 (b) 17 (c) 16 (d) 15
  18. 18.What is the 22nd term of the AP 10, 19, 28, 37, …? (a) 199 (b) 208 (c) 198 (d) 189
  19. 19.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 27 (c) 210 (d) 196
  20. 20.What is the sum of all the whole numbers from 1 to 68? (a) 2278 (b) 4692 (c) 2312 (d) 2346
  21. 21.What is the sum of all the whole numbers from 1 to 43? (a) 1892 (b) 947 (c) 903 (d) 946
  22. 22.What is the 27th term of the AP 3, 7, 11, 15, …? (a) 104 (b) 107 (c) 111 (d) 108
  23. 23.What is the 20th term of the AP 15, 17, 19, 21, …? (a) 38 (b) 53 (c) 40 (d) 55
  24. 24.Which term of the AP 7, 12, 17, 22, … is 57? (a) 11th (b) 12th (c) 10th (d) 13th
  25. 25.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 15 (c) 9 (d) 30
  26. 26.What is the missing term in the AP 18, 21, 24, ?, 30? (a) 28 (b) 30 (c) 27 (d) 26
  27. 27.What is the sum of all the whole numbers from 1 to 49? (a) 1226 (b) 2450 (c) 1225 (d) 1176
  28. 28.What is the 13th term of the AP 13, 15, 17, 19, …? (a) 39 (b) 24 (c) 37 (d) 26
  29. 29.What is the missing term in the AP 18, 22, 26, ?, 34? (a) 31 (b) 30 (c) 29 (d) 34
  30. 30.What is the sum of the first 10 terms of the AP 10, 14, 18, …? (a) 560 (b) 300 (c) 280 (d) 46
  31. 31.What is the sum of all the whole numbers from 1 to 55? (a) 1485 (b) 1540 (c) 1541 (d) 3080
  32. 32.Which term of the AP 4, 6, 8, 10, … is 70? (a) 36th (b) 33rd (c) 35th (d) 34th
  33. 33.Which term of the AP 20, 25, 30, 35, … is 95? (a) 19th (b) 16th (c) 15th (d) 17th
  34. 34.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 306 (b) 279 (c) 55 (d) 558
  35. 35.What is the sum of the first 12 terms of the AP 3, 9, 15, …? (a) 432 (b) 69 (c) 864 (d) 468
  36. 36.Which term of the AP 1, 3, 5, 7, … is 17? (a) 10th (b) 9th (c) 8th (d) 11th
  37. 37.What is the 11th term of the AP 2, 4, 6, 8, …? (a) 20 (b) 22 (c) 24 (d) 23
  38. 38.What is the missing term in the AP 16, ?, 34, 43, 52? (a) 34 (b) 26 (c) 24 (d) 25
  39. 39.What is the 26th term of the AP 7, 14, 21, 28, …? (a) 189 (b) 175 (c) 183 (d) 182
  40. 40.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 351 (c) 51 (d) 676

Answer key

  1. 2278
  2. 121
  3. 187
  4. 39
  5. 49
  6. 247
  7. 15
  8. 270
  9. 218
  10. 480
  11. 171
  12. 100
  13. 55
  14. 235
  15. 66
  16. 190
  17. 16
  18. 199
  19. 196
  20. 2346
  21. 946
  22. 107
  23. 53
  24. 11th
  25. 25
  26. 27
  27. 1225
  28. 37
  29. 30
  30. 280
  31. 1540
  32. 34th
  33. 16th
  34. 279
  35. 432
  36. 9th
  37. 22
  38. 25
  39. 182
  40. 676

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