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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 105 · 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 93? (a) 8742 (b) 4372 (c) 4371 (d) 4278
  2. 2.What is the 12th term of the AP 17, 19, 21, 23, …? (a) 41 (b) 24 (c) 39 (d) 22
  3. 3.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 38 (b) 161 (c) 322 (d) 166
  4. 4.What is the sum of the first 9 terms of the AP 8, 12, 16, …? (a) 432 (b) 40 (c) 216 (d) 234
  5. 5.What is the sum of the first 9 terms of the AP 7, 9, 11, …? (a) 270 (b) 23 (c) 144 (d) 135
  6. 6.What is the missing term in the AP 3, 9, ?, 21, 27? (a) 16 (b) 14 (c) 15 (d) 21
  7. 7.Which term of the AP 6, 11, 16, 21, … is 96? (a) 20th (b) 18th (c) 21st (d) 19th
  8. 8.What is the sum of the first 9 terms of the AP 2, 5, 8, …? (a) 26 (b) 126 (c) 252 (d) 129
  9. 9.What is the sum of the first 5 terms of the AP 7, 9, 11, …? (a) 60 (b) 15 (c) 110 (d) 55
  10. 10.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 105 (c) 210 (d) 196
  11. 11.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 66 (b) 132 (c) 78 (d) 21
  12. 12.What is the 36th term of the AP 7, 14, 21, 28, …? (a) 245 (b) 253 (c) 259 (d) 252
  13. 13.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 272 (c) 31 (d) 256
  14. 14.Which term of the AP 7, 10, 13, 16, … is 100? (a) 33rd (b) 31st (c) 32nd (d) 34th
  15. 15.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 36 (c) 64 (d) 15
  16. 16.What is the 15th term of the AP 5, 13, 21, 29, …? (a) 112 (b) 117 (c) 120 (d) 125
  17. 17.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 105 (b) 210 (c) 25 (d) 114
  18. 18.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 552 (c) 45 (d) 276
  19. 19.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 50 (b) 12 (c) 100 (d) 51
  20. 20.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 522 (b) 261 (c) 266 (d) 49
  21. 21.Which term of the AP 12, 21, 30, 39, … is 291? (a) 34th (b) 32nd (c) 33rd (d) 31st
  22. 22.What is the sum of the first 12 terms of the AP 3, 8, 13, …? (a) 732 (b) 396 (c) 58 (d) 366
  23. 23.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 406 (c) 812 (d) 378
  24. 24.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 350 (b) 62 (c) 380 (d) 700
  25. 25.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 110 (d) 100
  26. 26.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 80 (b) 160 (c) 95 (d) 28
  27. 27.What is the 13th term of the AP 20, 27, 34, 41, …? (a) 84 (b) 104 (c) 111 (d) 91
  28. 28.What is the sum of all the whole numbers from 1 to 54? (a) 1485 (b) 2970 (c) 1458 (d) 1431
  29. 29.What is the missing term in the AP 14, 19, 24, ?, 34? (a) 28 (b) 30 (c) 29 (d) 34
  30. 30.What is the 29th term of the AP 9, 13, 17, 21, …? (a) 112 (b) 125 (c) 121 (d) 116
  31. 31.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 50 (b) 30 (c) 25 (d) 9
  32. 32.What is the 40th term of the AP 20, 23, 26, 29, …? (a) 137 (b) 117 (c) 140 (d) 120
  33. 33.What is the missing term in the AP 14, ?, 18, 20, 22? (a) 16 (b) 15 (c) 17 (d) 18
  34. 34.What is the missing term in the AP 7, ?, 17, 22, 27? (a) 17 (b) 11 (c) 12 (d) 13
  35. 35.What is the 18th term of the AP 6, 10, 14, 18, …? (a) 68 (b) 74 (c) 78 (d) 72
  36. 36.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 90 (d) 81
  37. 37.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 342 (b) 189 (c) 35 (d) 171
  38. 38.What is the missing term in the AP 11, 14, 17, ?, 23? (a) 23 (b) 21 (c) 19 (d) 20
  39. 39.What is the 23rd term of the AP 9, 15, 21, 27, …? (a) 147 (b) 132 (c) 138 (d) 141
  40. 40.What is the sum of all the whole numbers from 1 to 94? (a) 4371 (b) 4418 (c) 4465 (d) 8930

Answer key

  1. 4371
  2. 39
  3. 161
  4. 216
  5. 135
  6. 15
  7. 19th
  8. 126
  9. 55
  10. 196
  11. 66
  12. 252
  13. 256
  14. 32nd
  15. 64
  16. 117
  17. 105
  18. 529
  19. 50
  20. 261
  21. 32nd
  22. 366
  23. 406
  24. 350
  25. 100
  26. 80
  27. 104
  28. 1485
  29. 29
  30. 121
  31. 25
  32. 137
  33. 16
  34. 12
  35. 74
  36. 81
  37. 171
  38. 20
  39. 141
  40. 4465

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