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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 427 · 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 1, 3, 5, …? (a) 25 (b) 9 (c) 30 (d) 50
  2. 2.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 17 (c) 81 (d) 45
  3. 3.What is the 34th term of the AP 4, 10, 16, 22, …? (a) 208 (b) 204 (c) 202 (d) 198
  4. 4.What is the 15th term of the AP 6, 10, 14, 18, …? (a) 62 (b) 56 (c) 60 (d) 66
  5. 5.What is the missing term in the AP 20, ?, 26, 29, 32? (a) 24 (b) 22 (c) 23 (d) 26
  6. 6.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 3916 (c) 3828 (d) 7832
  7. 7.What is the 39th term of the AP 2, 9, 16, 23, …? (a) 266 (b) 273 (c) 275 (d) 268
  8. 8.What is the sum of all the whole numbers from 1 to 64? (a) 2016 (b) 2048 (c) 2080 (d) 4160
  9. 9.What is the 11th term of the AP 2, 7, 12, 17, …? (a) 55 (b) 52 (c) 50 (d) 57
  10. 10.What is the missing term in the AP 7, 14, 21, ?, 35? (a) 27 (b) 35 (c) 28 (d) 29
  11. 11.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 930 (c) 900 (d) 59
  12. 12.Which term of the AP 15, 19, 23, 27, … is 79? (a) 19th (b) 17th (c) 16th (d) 18th
  13. 13.What is the 36th term of the AP 13, 20, 27, 34, …? (a) 245 (b) 265 (c) 252 (d) 258
  14. 14.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 160 (b) 145 (c) 28 (d) 290
  15. 15.What is the 19th term of the AP 2, 8, 14, 20, …? (a) 114 (b) 110 (c) 116 (d) 108
  16. 16.What is the sum of the first 12 terms of the AP 4, 10, 16, …? (a) 480 (b) 70 (c) 888 (d) 444
  17. 17.What is the 21st term of the AP 20, 22, 24, 26, …? (a) 60 (b) 62 (c) 40 (d) 42
  18. 18.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 276 (c) 552 (d) 529
  19. 19.What is the 14th term of the AP 4, 12, 20, 28, …? (a) 116 (b) 112 (c) 104 (d) 108
  20. 20.What is the 26th term of the AP 8, 15, 22, 29, …? (a) 190 (b) 182 (c) 183 (d) 175
  21. 21.What is the sum of the first 9 terms of the AP 7, 9, 11, …? (a) 270 (b) 23 (c) 135 (d) 144
  22. 22.What is the sum of all the whole numbers from 1 to 54? (a) 1431 (b) 2970 (c) 1485 (d) 1458
  23. 23.What is the missing term in the AP 14, 22, 30, ?, 46? (a) 37 (b) 39 (c) 46 (d) 38
  24. 24.What is the missing term in the AP 18, ?, 28, 33, 38? (a) 22 (b) 28 (c) 23 (d) 24
  25. 25.What is the 33rd term of the AP 8, 16, 24, 32, …? (a) 264 (b) 265 (c) 272 (d) 256
  26. 26.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 210 (c) 420 (d) 400
  27. 27.What is the 14th term of the AP 5, 14, 23, 32, …? (a) 117 (b) 131 (c) 126 (d) 122
  28. 28.What is the 18th term of the AP 12, 18, 24, 30, …? (a) 108 (b) 114 (c) 102 (d) 120
  29. 29.What is the sum of all the whole numbers from 1 to 91? (a) 8372 (b) 4187 (c) 4095 (d) 4186
  30. 30.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 32 (b) 102 (c) 204 (d) 120
  31. 31.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 19 (d) 100
  32. 32.What is the 14th term of the AP 17, 22, 27, 32, …? (a) 70 (b) 82 (c) 65 (d) 87
  33. 33.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 43 (c) 253 (d) 484
  34. 34.What is the missing term in the AP 9, 18, 27, ?, 45? (a) 45 (b) 35 (c) 37 (d) 36
  35. 35.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 346 (b) 56 (c) 341 (d) 682
  36. 36.What is the sum of the first 8 terms of the AP 9, 11, 13, …? (a) 136 (b) 23 (c) 128 (d) 256
  37. 37.What is the sum of the first 11 terms of the AP 8, 10, 12, …? (a) 28 (b) 396 (c) 209 (d) 198
  38. 38.What is the sum of the first 9 terms of the AP 8, 10, 12, …? (a) 144 (b) 153 (c) 24 (d) 288
  39. 39.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 462 (d) 441
  40. 40.What is the sum of the first 12 terms of the AP 6, 8, 10, …? (a) 28 (b) 408 (c) 216 (d) 204

Answer key

  1. 25
  2. 81
  3. 202
  4. 62
  5. 23
  6. 3916
  7. 268
  8. 2080
  9. 52
  10. 28
  11. 900
  12. 17th
  13. 258
  14. 145
  15. 110
  16. 444
  17. 60
  18. 529
  19. 108
  20. 183
  21. 135
  22. 1485
  23. 38
  24. 23
  25. 264
  26. 400
  27. 122
  28. 114
  29. 4186
  30. 102
  31. 100
  32. 82
  33. 484
  34. 36
  35. 341
  36. 128
  37. 198
  38. 144
  39. 441
  40. 204

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