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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 363 · 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 2, 5, 8, …? (a) 43 (b) 80 (c) 14 (d) 40
  2. 2.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 153 (c) 33 (d) 306
  3. 3.What is the sum of all the whole numbers from 1 to 14? (a) 98 (b) 210 (c) 105 (d) 91
  4. 4.What is the sum of all the whole numbers from 1 to 50? (a) 1275 (b) 1225 (c) 1250 (d) 2550
  5. 5.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 45 (b) 216 (c) 192 (d) 384
  6. 6.What is the 16th term of the AP 13, 17, 21, 25, …? (a) 60 (b) 73 (c) 64 (d) 77
  7. 7.What is the 11th term of the AP 2, 4, 6, 8, …? (a) 23 (b) 20 (c) 22 (d) 24
  8. 8.What is the missing term in the AP 9, 16, ?, 30, 37? (a) 30 (b) 23 (c) 24 (d) 22
  9. 9.What is the missing term in the AP 18, 27, 36, ?, 54? (a) 45 (b) 46 (c) 54 (d) 44
  10. 10.Which term of the AP 12, 19, 26, 33, … is 264? (a) 37th (b) 36th (c) 39th (d) 38th
  11. 11.Which term of the AP 13, 18, 23, 28, … is 128? (a) 24th (b) 26th (c) 25th (d) 23rd
  12. 12.What is the 16th term of the AP 8, 16, 24, 32, …? (a) 128 (b) 136 (c) 129 (d) 120
  13. 13.What is the sum of all the whole numbers from 1 to 60? (a) 3660 (b) 1830 (c) 1800 (d) 1770
  14. 14.What is the 23rd term of the AP 3, 12, 21, 30, …? (a) 207 (b) 210 (c) 198 (d) 201
  15. 15.What is the sum of the first 12 terms of the AP 7, 11, 15, …? (a) 696 (b) 51 (c) 372 (d) 348
  16. 16.What is the 25th term of the AP 11, 20, 29, 38, …? (a) 216 (b) 225 (c) 236 (d) 227
  17. 17.What is the 16th term of the AP 1, 7, 13, 19, …? (a) 91 (b) 96 (c) 90 (d) 97
  18. 18.What is the 39th term of the AP 13, 18, 23, 28, …? (a) 203 (b) 195 (c) 208 (d) 190
  19. 19.What is the 24th term of the AP 3, 9, 15, 21, …? (a) 144 (b) 138 (c) 147 (d) 141
  20. 20.What is the sum of all the whole numbers from 1 to 69? (a) 2416 (b) 2346 (c) 2415 (d) 4830
  21. 21.What is the 29th term of the AP 6, 11, 16, 21, …? (a) 140 (b) 151 (c) 145 (d) 146
  22. 22.What is the sum of the first 5 terms of the AP 6, 10, 14, …? (a) 140 (b) 70 (c) 22 (d) 80
  23. 23.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 625 (c) 325 (d) 650
  24. 24.What is the 25th term of the AP 17, 20, 23, 26, …? (a) 92 (b) 72 (c) 89 (d) 75
  25. 25.What is the sum of all the whole numbers from 1 to 97? (a) 9506 (b) 4656 (c) 4753 (d) 4754
  26. 26.What is the 13th term of the AP 18, 21, 24, 27, …? (a) 57 (b) 54 (c) 39 (d) 36
  27. 27.What is the missing term in the AP 9, ?, 19, 24, 29? (a) 13 (b) 15 (c) 14 (d) 19
  28. 28.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 182 (c) 169 (d) 91
  29. 29.What is the 22nd term of the AP 9, 18, 27, 36, …? (a) 189 (b) 207 (c) 199 (d) 198
  30. 30.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 15 (c) 30 (d) 9
  31. 31.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 13 (b) 56 (c) 98 (d) 49
  32. 32.What is the sum of all the whole numbers from 1 to 54? (a) 1431 (b) 1485 (c) 1458 (d) 2970
  33. 33.What is the missing term in the AP 4, 10, ?, 22, 28? (a) 16 (b) 17 (c) 15 (d) 22
  34. 34.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 34 (b) 114 (c) 132 (d) 228
  35. 35.Which term of the AP 4, 12, 20, 28, … is 164? (a) 22nd (b) 21st (c) 23rd (d) 20th
  36. 36.What is the 36th term of the AP 16, 18, 20, 22, …? (a) 72 (b) 88 (c) 70 (d) 86
  37. 37.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 558 (b) 279 (c) 306 (d) 55
  38. 38.What is the sum of the first 7 terms of the AP 9, 12, 15, …? (a) 129 (b) 27 (c) 252 (d) 126
  39. 39.What is the sum of all the whole numbers from 1 to 53? (a) 1378 (b) 1432 (c) 2862 (d) 1431
  40. 40.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 190 (b) 350 (c) 31 (d) 175

Answer key

  1. 40
  2. 289
  3. 105
  4. 1275
  5. 192
  6. 73
  7. 22
  8. 23
  9. 45
  10. 37th
  11. 24th
  12. 128
  13. 1830
  14. 201
  15. 348
  16. 227
  17. 91
  18. 203
  19. 141
  20. 2415
  21. 146
  22. 70
  23. 625
  24. 89
  25. 4753
  26. 54
  27. 14
  28. 169
  29. 198
  30. 25
  31. 49
  32. 1485
  33. 16
  34. 114
  35. 21st
  36. 86
  37. 279
  38. 126
  39. 1431
  40. 175

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