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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 481 · 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 7, ?, 21, 28, 35? (a) 14 (b) 21 (c) 15 (d) 13
  2. 2.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 19 (c) 110 (d) 100
  3. 3.What is the 21st term of the AP 6, 8, 10, 12, …? (a) 42 (b) 48 (c) 46 (d) 40
  4. 4.What is the 19th term of the AP 5, 13, 21, 29, …? (a) 149 (b) 152 (c) 144 (d) 157
  5. 5.What is the sum of all the whole numbers from 1 to 26? (a) 338 (b) 702 (c) 351 (d) 325
  6. 6.What is the 30th term of the AP 1, 5, 9, 13, …? (a) 117 (b) 121 (c) 120 (d) 116
  7. 7.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 57 (c) 870 (d) 841
  8. 8.What is the 21st term of the AP 9, 14, 19, 24, …? (a) 114 (b) 109 (c) 105 (d) 100
  9. 9.What is the 16th term of the AP 14, 22, 30, 38, …? (a) 120 (b) 134 (c) 128 (d) 142
  10. 10.What is the missing term in the AP 17, ?, 23, 26, 29? (a) 19 (b) 20 (c) 21 (d) 23
  11. 11.Which term of the AP 17, 21, 25, 29, … is 73? (a) 16th (b) 15th (c) 17th (d) 14th
  12. 12.What is the 38th term of the AP 13, 22, 31, 40, …? (a) 355 (b) 333 (c) 346 (d) 342
  13. 13.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 24 (b) 105 (c) 210 (d) 108
  14. 14.What is the sum of the first 8 terms of the AP 5, 6, 7, …? (a) 12 (b) 72 (c) 68 (d) 136
  15. 15.What is the 25th term of the AP 14, 23, 32, 41, …? (a) 225 (b) 216 (c) 239 (d) 230
  16. 16.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 144 (b) 72 (c) 80 (d) 16
  17. 17.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 121 (c) 21 (d) 132
  18. 18.What is the sum of all the whole numbers from 1 to 25? (a) 650 (b) 325 (c) 300 (d) 326
  19. 19.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 184 (b) 96 (c) 15 (d) 92
  20. 20.What is the 22nd term of the AP 15, 22, 29, 36, …? (a) 154 (b) 169 (c) 162 (d) 147
  21. 21.Which term of the AP 13, 19, 25, 31, … is 175? (a) 30th (b) 29th (c) 28th (d) 27th
  22. 22.What is the sum of the first 10 terms of the AP 8, 9, 10, …? (a) 125 (b) 17 (c) 250 (d) 130
  23. 23.What is the missing term in the AP 12, 14, ?, 18, 20? (a) 15 (b) 17 (c) 18 (d) 16
  24. 24.What is the 14th term of the AP 5, 11, 17, 23, …? (a) 78 (b) 84 (c) 83 (d) 89
  25. 25.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 351 (c) 51 (d) 676
  26. 26.What is the sum of all the whole numbers from 1 to 53? (a) 1378 (b) 1432 (c) 1431 (d) 2862
  27. 27.What is the sum of the first 6 terms of the AP 4, 7, 10, …? (a) 138 (b) 78 (c) 19 (d) 69
  28. 28.What is the sum of all the whole numbers from 1 to 56? (a) 1540 (b) 1568 (c) 1596 (d) 3192
  29. 29.What is the 33rd term of the AP 1, 4, 7, 10, …? (a) 96 (b) 100 (c) 97 (d) 99
  30. 30.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 36 (c) 21 (d) 42
  31. 31.Which term of the AP 1, 7, 13, 19, … is 145? (a) 24th (b) 27th (c) 25th (d) 26th
  32. 32.What is the sum of the first 9 terms of the AP 8, 13, 18, …? (a) 504 (b) 252 (c) 48 (d) 257
  33. 33.What is the missing term in the AP 6, ?, 14, 18, 22? (a) 9 (b) 10 (c) 11 (d) 14
  34. 34.What is the sum of all the whole numbers from 1 to 48? (a) 1152 (b) 2352 (c) 1176 (d) 1128
  35. 35.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 15 (c) 36 (d) 72
  36. 36.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 294 (b) 168 (c) 147 (d) 39
  37. 37.What is the missing term in the AP 13, 15, ?, 19, 21? (a) 16 (b) 17 (c) 19 (d) 18
  38. 38.What is the sum of the first 9 terms of the AP 7, 11, 15, …? (a) 207 (b) 225 (c) 414 (d) 39
  39. 39.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 930 (c) 900 (d) 59
  40. 40.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 346 (b) 682 (c) 341 (d) 56

Answer key

  1. 14
  2. 100
  3. 46
  4. 149
  5. 351
  6. 117
  7. 841
  8. 109
  9. 134
  10. 20
  11. 15th
  12. 346
  13. 105
  14. 68
  15. 230
  16. 72
  17. 121
  18. 325
  19. 92
  20. 162
  21. 28th
  22. 125
  23. 16
  24. 83
  25. 676
  26. 1431
  27. 69
  28. 1596
  29. 97
  30. 36
  31. 25th
  32. 252
  33. 10
  34. 1176
  35. 64
  36. 147
  37. 17
  38. 207
  39. 900
  40. 341

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