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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 94 · 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 9, 10, 11, …? (a) 56 (b) 110 (c) 13 (d) 55
  2. 2.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 216 (b) 112 (c) 108 (d) 17
  3. 3.What is the 20th term of the AP 6, 9, 12, 15, …? (a) 60 (b) 66 (c) 57 (d) 63
  4. 4.What is the 17th term of the AP 11, 17, 23, 29, …? (a) 102 (b) 96 (c) 107 (d) 113
  5. 5.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 100 (d) 110
  6. 6.What is the missing term in the AP 8, ?, 16, 20, 24? (a) 11 (b) 12 (c) 16 (d) 13
  7. 7.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 126 (b) 15 (c) 70 (d) 63
  8. 8.What is the sum of the first 10 terms of the AP 7, 10, 13, …? (a) 205 (b) 220 (c) 410 (d) 34
  9. 9.What is the sum of all the whole numbers from 1 to 60? (a) 1800 (b) 1770 (c) 1830 (d) 3660
  10. 10.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 870 (c) 841 (d) 57
  11. 11.What is the 32nd term of the AP 20, 23, 26, 29, …? (a) 96 (b) 93 (c) 113 (d) 116
  12. 12.What is the sum of the first 8 terms of the AP 5, 11, 17, …? (a) 208 (b) 416 (c) 232 (d) 47
  13. 13.What is the sum of all the whole numbers from 1 to 92? (a) 4278 (b) 4232 (c) 8556 (d) 4186
  14. 14.What is the sum of all the whole numbers from 1 to 26? (a) 338 (b) 702 (c) 351 (d) 325
  15. 15.What is the sum of the first 7 terms of the AP 8, 10, 12, …? (a) 105 (b) 20 (c) 196 (d) 98
  16. 16.Which term of the AP 7, 11, 15, 19, … is 103? (a) 24th (b) 25th (c) 27th (d) 26th
  17. 17.What is the sum of all the whole numbers from 1 to 47? (a) 1129 (b) 2256 (c) 1128 (d) 1081
  18. 18.What is the 14th term of the AP 8, 16, 24, 32, …? (a) 104 (b) 120 (c) 113 (d) 112
  19. 19.What is the 22nd term of the AP 8, 10, 12, 14, …? (a) 52 (b) 42 (c) 44 (d) 50
  20. 20.What is the 40th term of the AP 1, 8, 15, 22, …? (a) 281 (b) 280 (c) 273 (d) 274
  21. 21.What is the sum of the first 7 terms of the AP 7, 10, 13, …? (a) 224 (b) 25 (c) 112 (d) 115
  22. 22.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 36 (c) 42 (d) 21
  23. 23.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 406 (c) 55 (d) 812
  24. 24.What is the 13th term of the AP 19, 25, 31, 37, …? (a) 72 (b) 97 (c) 78 (d) 91
  25. 25.What is the sum of the first 8 terms of the AP 6, 10, 14, …? (a) 320 (b) 34 (c) 176 (d) 160
  26. 26.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 379 (c) 378 (d) 756
  27. 27.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 40 (b) 70 (c) 35 (d) 11
  28. 28.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 136 (b) 272 (c) 144 (d) 24
  29. 29.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 90 (c) 45 (d) 81
  30. 30.What is the 24th term of the AP 12, 17, 22, 27, …? (a) 120 (b) 115 (c) 127 (d) 132
  31. 31.Which term of the AP 2, 11, 20, 29, … is 227? (a) 28th (b) 26th (c) 27th (d) 25th
  32. 32.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 380 (c) 37 (d) 190
  33. 33.What is the missing term in the AP 9, 17, ?, 33, 41? (a) 33 (b) 24 (c) 25 (d) 26
  34. 34.What is the 15th term of the AP 2, 10, 18, 26, …? (a) 114 (b) 122 (c) 120 (d) 112
  35. 35.Which term of the AP 8, 12, 16, 20, … is 36? (a) 10th (b) 7th (c) 9th (d) 8th
  36. 36.What is the 38th term of the AP 17, 26, 35, 44, …? (a) 359 (b) 342 (c) 333 (d) 350
  37. 37.What is the 38th term of the AP 17, 20, 23, 26, …? (a) 111 (b) 128 (c) 131 (d) 114
  38. 38.What is the 28th term of the AP 12, 18, 24, 30, …? (a) 180 (b) 162 (c) 168 (d) 174
  39. 39.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 21 (b) 78 (c) 132 (d) 66
  40. 40.What is the 13th term of the AP 2, 5, 8, 11, …? (a) 38 (b) 39 (c) 36 (d) 41

Answer key

  1. 55
  2. 108
  3. 63
  4. 107
  5. 100
  6. 12
  7. 63
  8. 205
  9. 1830
  10. 841
  11. 113
  12. 208
  13. 4278
  14. 351
  15. 98
  16. 25th
  17. 1128
  18. 112
  19. 50
  20. 274
  21. 112
  22. 36
  23. 784
  24. 91
  25. 160
  26. 378
  27. 35
  28. 136
  29. 81
  30. 127
  31. 26th
  32. 361
  33. 25
  34. 114
  35. 8th
  36. 350
  37. 128
  38. 174
  39. 66
  40. 38

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