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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 563 · 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 40? (a) 1640 (b) 820 (c) 800 (d) 780
  2. 2.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 88 (b) 9 (c) 44 (d) 48
  3. 3.What is the 37th term of the AP 9, 14, 19, 24, …? (a) 189 (b) 180 (c) 185 (d) 194
  4. 4.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 45 (c) 552 (d) 276
  5. 5.What is the 15th term of the AP 1, 6, 11, 16, …? (a) 75 (b) 76 (c) 70 (d) 71
  6. 6.What is the missing term in the AP 14, ?, 32, 41, 50? (a) 32 (b) 23 (c) 24 (d) 22
  7. 7.What is the 26th term of the AP 16, 25, 34, 43, …? (a) 225 (b) 250 (c) 241 (d) 234
  8. 8.What is the sum of the first 7 terms of the AP 9, 13, 17, …? (a) 147 (b) 161 (c) 294 (d) 33
  9. 9.What is the missing term in the AP 6, 10, 14, ?, 22? (a) 19 (b) 22 (c) 17 (d) 18
  10. 10.Which term of the AP 16, 23, 30, 37, … is 156? (a) 20th (b) 22nd (c) 23rd (d) 21st
  11. 11.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 17 (b) 66 (c) 57 (d) 114
  12. 12.What is the sum of the first 10 terms of the AP 1, 5, 9, …? (a) 190 (b) 210 (c) 37 (d) 380
  13. 13.What is the sum of all the whole numbers from 1 to 69? (a) 4830 (b) 2416 (c) 2346 (d) 2415
  14. 14.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 45 (c) 90 (d) 81
  15. 15.What is the 10th term of the AP 9, 11, 13, 15, …? (a) 27 (b) 18 (c) 29 (d) 20
  16. 16.What is the sum of the first 10 terms of the AP 6, 7, 8, …? (a) 15 (b) 110 (c) 210 (d) 105
  17. 17.What is the 19th term of the AP 9, 15, 21, 27, …? (a) 108 (b) 114 (c) 117 (d) 123
  18. 18.What is the 26th term of the AP 15, 21, 27, 33, …? (a) 171 (b) 150 (c) 165 (d) 156
  19. 19.What is the sum of all the whole numbers from 1 to 58? (a) 1653 (b) 1682 (c) 1711 (d) 3422
  20. 20.What is the sum of the first 11 terms of the AP 5, 8, 11, …? (a) 223 (b) 220 (c) 35 (d) 440
  21. 21.What is the sum of the first 7 terms of the AP 9, 14, 19, …? (a) 173 (b) 168 (c) 336 (d) 39
  22. 22.Which term of the AP 14, 17, 20, 23, … is 86? (a) 26th (b) 24th (c) 25th (d) 27th
  23. 23.What is the sum of all the whole numbers from 1 to 10? (a) 55 (b) 50 (c) 45 (d) 110
  24. 24.What is the 22nd term of the AP 9, 18, 27, 36, …? (a) 199 (b) 207 (c) 189 (d) 198
  25. 25.What is the 39th term of the AP 5, 14, 23, 32, …? (a) 342 (b) 351 (c) 347 (d) 356
  26. 26.What is the 14th term of the AP 20, 28, 36, 44, …? (a) 132 (b) 112 (c) 124 (d) 104
  27. 27.What is the 36th term of the AP 11, 15, 19, 23, …? (a) 155 (b) 140 (c) 151 (d) 144
  28. 28.What is the 26th term of the AP 8, 11, 14, 17, …? (a) 83 (b) 86 (c) 78 (d) 75
  29. 29.What is the sum of the first 5 terms of the AP 3, 9, 15, …? (a) 75 (b) 90 (c) 27 (d) 150
  30. 30.What is the 40th term of the AP 4, 12, 20, 28, …? (a) 312 (b) 324 (c) 316 (d) 320
  31. 31.What is the sum of the first 11 terms of the AP 7, 12, 17, …? (a) 704 (b) 357 (c) 57 (d) 352
  32. 32.What is the sum of all the whole numbers from 1 to 71? (a) 2485 (b) 2556 (c) 2557 (d) 5112
  33. 33.What is the 19th term of the AP 1, 4, 7, 10, …? (a) 55 (b) 57 (c) 58 (d) 54
  34. 34.What is the sum of the first 5 terms of the AP 10, 14, 18, …? (a) 26 (b) 180 (c) 100 (d) 90
  35. 35.What is the 17th term of the AP 18, 23, 28, 33, …? (a) 103 (b) 80 (c) 85 (d) 98
  36. 36.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 210 (b) 420 (c) 228 (d) 34
  37. 37.What is the sum of all the whole numbers from 1 to 55? (a) 1540 (b) 1485 (c) 1541 (d) 3080
  38. 38.What is the 14th term of the AP 4, 13, 22, 31, …? (a) 126 (b) 130 (c) 121 (d) 117
  39. 39.Which term of the AP 14, 22, 30, 38, … is 86? (a) 12th (b) 9th (c) 10th (d) 11th
  40. 40.What is the 10th term of the AP 15, 18, 21, 24, …? (a) 45 (b) 42 (c) 30 (d) 27

Answer key

  1. 820
  2. 44
  3. 189
  4. 529
  5. 71
  6. 23
  7. 241
  8. 147
  9. 18
  10. 21st
  11. 57
  12. 190
  13. 2415
  14. 81
  15. 27
  16. 105
  17. 117
  18. 165
  19. 1711
  20. 220
  21. 168
  22. 25th
  23. 55
  24. 198
  25. 347
  26. 124
  27. 151
  28. 83
  29. 75
  30. 316
  31. 352
  32. 2556
  33. 55
  34. 90
  35. 98
  36. 210
  37. 1540
  38. 121
  39. 10th
  40. 42

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