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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 509 · 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 20? (a) 190 (b) 420 (c) 200 (d) 210
  2. 2.What is the 13th term of the AP 13, 16, 19, 22, …? (a) 52 (b) 39 (c) 49 (d) 36
  3. 3.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 1056 (c) 496 (d) 528
  4. 4.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 300 (c) 600 (d) 47
  5. 5.What is the 38th term of the AP 13, 21, 29, 37, …? (a) 296 (b) 317 (c) 304 (d) 309
  6. 6.What is the 14th term of the AP 20, 23, 26, 29, …? (a) 39 (b) 42 (c) 59 (d) 62
  7. 7.What is the missing term in the AP 9, 16, ?, 30, 37? (a) 23 (b) 22 (c) 30 (d) 24
  8. 8.What is the sum of the first 7 terms of the AP 5, 9, 13, …? (a) 29 (b) 119 (c) 238 (d) 133
  9. 9.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 9 (c) 15 (d) 25
  10. 10.What is the sum of all the whole numbers from 1 to 17? (a) 136 (b) 154 (c) 153 (d) 306
  11. 11.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 96 (b) 180 (c) 20 (d) 90
  12. 12.What is the 39th term of the AP 19, 24, 29, 34, …? (a) 214 (b) 195 (c) 209 (d) 190
  13. 13.Which term of the AP 10, 12, 14, 16, … is 42? (a) 18th (b) 21st (c) 17th (d) 16th
  14. 14.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 75 (b) 1008 (c) 540 (d) 504
  15. 15.What is the missing term in the AP 2, ?, 18, 26, 34? (a) 18 (b) 10 (c) 9 (d) 11
  16. 16.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 100 (d) 19
  17. 17.Which term of the AP 2, 4, 6, 8, … is 50? (a) 27th (b) 26th (c) 24th (d) 25th
  18. 18.What is the 13th term of the AP 20, 25, 30, 35, …? (a) 60 (b) 85 (c) 65 (d) 80
  19. 19.What is the sum of all the whole numbers from 1 to 49? (a) 1225 (b) 2450 (c) 1226 (d) 1176
  20. 20.What is the sum of the first 9 terms of the AP 4, 9, 14, …? (a) 432 (b) 221 (c) 44 (d) 216
  21. 21.Which term of the AP 16, 19, 22, 25, … is 61? (a) 18th (b) 16th (c) 15th (d) 17th
  22. 22.What is the sum of the first 11 terms of the AP 8, 12, 16, …? (a) 616 (b) 308 (c) 330 (d) 48
  23. 23.What is the missing term in the AP 9, ?, 15, 18, 21? (a) 15 (b) 11 (c) 12 (d) 13
  24. 24.What is the 13th term of the AP 17, 23, 29, 35, …? (a) 72 (b) 78 (c) 95 (d) 89
  25. 25.What is the sum of all the whole numbers from 1 to 71? (a) 2556 (b) 2557 (c) 2485 (d) 5112
  26. 26.What is the sum of the first 9 terms of the AP 10, 14, 18, …? (a) 468 (b) 234 (c) 252 (d) 42
  27. 27.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 34 (b) 162 (c) 324 (d) 180
  28. 28.What is the sum of all the whole numbers from 1 to 16? (a) 128 (b) 272 (c) 136 (d) 120
  29. 29.What is the 20th term of the AP 12, 14, 16, 18, …? (a) 40 (b) 38 (c) 52 (d) 50
  30. 30.What is the sum of the first 11 terms of the AP 4, 9, 14, …? (a) 54 (b) 324 (c) 319 (d) 638
  31. 31.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 21 (c) 121 (d) 66
  32. 32.What is the 36th term of the AP 16, 18, 20, 22, …? (a) 72 (b) 86 (c) 70 (d) 88
  33. 33.What is the sum of the first 11 terms of the AP 9, 12, 15, …? (a) 267 (b) 528 (c) 39 (d) 264
  34. 34.What is the 34th term of the AP 3, 11, 19, 27, …? (a) 272 (b) 264 (c) 275 (d) 267
  35. 35.What is the missing term in the AP 18, 20, ?, 24, 26? (a) 21 (b) 24 (c) 23 (d) 22
  36. 36.What is the 20th term of the AP 10, 12, 14, 16, …? (a) 38 (b) 48 (c) 40 (d) 50
  37. 37.What is the 16th term of the AP 8, 16, 24, 32, …? (a) 136 (b) 128 (c) 120 (d) 129
  38. 38.What is the 38th term of the AP 4, 7, 10, 13, …? (a) 111 (b) 115 (c) 114 (d) 118
  39. 39.What is the sum of the first 7 terms of the AP 5, 8, 11, …? (a) 196 (b) 98 (c) 23 (d) 101
  40. 40.What is the 20th term of the AP 6, 15, 24, 33, …? (a) 171 (b) 177 (c) 186 (d) 180

Answer key

  1. 210
  2. 49
  3. 528
  4. 576
  5. 309
  6. 59
  7. 23
  8. 119
  9. 25
  10. 153
  11. 90
  12. 209
  13. 17th
  14. 504
  15. 10
  16. 100
  17. 25th
  18. 80
  19. 1225
  20. 216
  21. 16th
  22. 308
  23. 12
  24. 89
  25. 2556
  26. 234
  27. 162
  28. 136
  29. 50
  30. 319
  31. 121
  32. 86
  33. 264
  34. 267
  35. 22
  36. 48
  37. 128
  38. 115
  39. 98
  40. 177

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