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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 235 · 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 missing term in the AP 16, 23, ?, 37, 44? (a) 30 (b) 31 (c) 29 (d) 37
  2. 2.Which term of the AP 17, 22, 27, 32, … is 77? (a) 13th (b) 15th (c) 12th (d) 14th
  3. 3.What is the sum of the first 7 terms of the AP 7, 10, 13, …? (a) 115 (b) 112 (c) 224 (d) 25
  4. 4.What is the 21st term of the AP 4, 12, 20, 28, …? (a) 164 (b) 172 (c) 160 (d) 168
  5. 5.What is the missing term in the AP 16, 24, 32, ?, 48? (a) 39 (b) 48 (c) 41 (d) 40
  6. 6.What is the 28th term of the AP 5, 13, 21, 29, …? (a) 216 (b) 229 (c) 224 (d) 221
  7. 7.Which term of the AP 8, 11, 14, 17, … is 44? (a) 13th (b) 14th (c) 15th (d) 12th
  8. 8.Which term of the AP 6, 13, 20, 27, … is 279? (a) 41st (b) 39th (c) 42nd (d) 40th
  9. 9.Which term of the AP 12, 14, 16, 18, … is 38? (a) 14th (b) 13th (c) 19th (d) 15th
  10. 10.What is the 21st term of the AP 18, 25, 32, 39, …? (a) 165 (b) 158 (c) 147 (d) 140
  11. 11.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 23 (d) 144
  12. 12.What is the sum of all the whole numbers from 1 to 55? (a) 1540 (b) 1485 (c) 3080 (d) 1541
  13. 13.What is the missing term in the AP 5, ?, 13, 17, 21? (a) 10 (b) 13 (c) 9 (d) 8
  14. 14.Which term of the AP 3, 8, 13, 18, … is 103? (a) 23rd (b) 20th (c) 22nd (d) 21st
  15. 15.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 39 (b) 210 (c) 420 (d) 230
  16. 16.What is the 38th term of the AP 19, 22, 25, 28, …? (a) 114 (b) 130 (c) 133 (d) 111
  17. 17.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 15 (d) 25
  18. 18.Which term of the AP 3, 10, 17, 24, … is 157? (a) 24th (b) 25th (c) 22nd (d) 23rd
  19. 19.What is the 15th term of the AP 3, 11, 19, 27, …? (a) 115 (b) 123 (c) 112 (d) 120
  20. 20.What is the 22nd term of the AP 2, 8, 14, 20, …? (a) 128 (b) 126 (c) 132 (d) 134
  21. 21.What is the sum of all the whole numbers from 1 to 39? (a) 1560 (b) 780 (c) 781 (d) 741
  22. 22.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 270 (b) 27 (c) 135 (d) 138
  23. 23.What is the 34th term of the AP 14, 20, 26, 32, …? (a) 198 (b) 204 (c) 218 (d) 212
  24. 24.Which term of the AP 15, 24, 33, 42, … is 213? (a) 25th (b) 24th (c) 23rd (d) 22nd
  25. 25.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 180 (b) 96 (c) 20 (d) 90
  26. 26.What is the sum of all the whole numbers from 1 to 33? (a) 562 (b) 528 (c) 561 (d) 1122
  27. 27.What is the missing term in the AP 19, 27, ?, 43, 51? (a) 35 (b) 43 (c) 34 (d) 36
  28. 28.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 13 (c) 56 (d) 49
  29. 29.Which term of the AP 7, 14, 21, 28, … is 70? (a) 9th (b) 12th (c) 10th (d) 11th
  30. 30.What is the sum of the first 10 terms of the AP 4, 10, 16, …? (a) 58 (b) 310 (c) 340 (d) 620
  31. 31.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 36 (c) 64 (d) 72
  32. 32.What is the sum of the first 9 terms of the AP 5, 9, 13, …? (a) 378 (b) 189 (c) 37 (d) 207
  33. 33.What is the 22nd term of the AP 4, 6, 8, 10, …? (a) 42 (b) 44 (c) 48 (d) 46
  34. 34.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 100 (c) 110 (d) 55
  35. 35.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 81 (c) 17 (d) 45
  36. 36.Which term of the AP 18, 24, 30, 36, … is 174? (a) 29th (b) 28th (c) 26th (d) 27th
  37. 37.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 31 (c) 272 (d) 136
  38. 38.What is the 24th term of the AP 2, 11, 20, 29, …? (a) 216 (b) 209 (c) 207 (d) 218
  39. 39.What is the 24th term of the AP 15, 19, 23, 27, …? (a) 111 (b) 96 (c) 107 (d) 92
  40. 40.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 63 (b) 363 (c) 396 (d) 726

Answer key

  1. 30
  2. 13th
  3. 112
  4. 164
  5. 40
  6. 221
  7. 13th
  8. 40th
  9. 14th
  10. 158
  11. 144
  12. 1540
  13. 9
  14. 21st
  15. 210
  16. 130
  17. 25
  18. 23rd
  19. 115
  20. 128
  21. 780
  22. 135
  23. 212
  24. 23rd
  25. 90
  26. 561
  27. 35
  28. 49
  29. 10th
  30. 310
  31. 64
  32. 189
  33. 46
  34. 100
  35. 81
  36. 27th
  37. 256
  38. 209
  39. 107
  40. 363

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