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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 117 · 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 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 342 (c) 171 (d) 324
  2. 2.What is the 28th term of the AP 5, 10, 15, 20, …? (a) 141 (b) 145 (c) 140 (d) 135
  3. 3.What is the missing term in the AP 5, 12, 19, ?, 33? (a) 33 (b) 25 (c) 26 (d) 27
  4. 4.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 6 (b) 42 (c) 24 (d) 21
  5. 5.Which term of the AP 19, 27, 35, 43, … is 123? (a) 15th (b) 13th (c) 14th (d) 16th
  6. 6.What is the sum of the first 10 terms of the AP 8, 11, 14, …? (a) 35 (b) 230 (c) 430 (d) 215
  7. 7.What is the sum of all the whole numbers from 1 to 54? (a) 1431 (b) 1485 (c) 1458 (d) 2970
  8. 8.What is the 21st term of the AP 8, 10, 12, 14, …? (a) 40 (b) 50 (c) 48 (d) 42
  9. 9.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 210 (b) 420 (c) 39 (d) 230
  10. 10.What is the sum of all the whole numbers from 1 to 89? (a) 3916 (b) 4006 (c) 4005 (d) 8010
  11. 11.What is the sum of the first 7 terms of the AP 3, 7, 11, …? (a) 210 (b) 119 (c) 105 (d) 27
  12. 12.What is the 30th term of the AP 6, 15, 24, 33, …? (a) 267 (b) 270 (c) 276 (d) 261
  13. 13.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 506 (c) 253 (d) 484
  14. 14.Which term of the AP 5, 8, 11, 14, … is 98? (a) 33rd (b) 32nd (c) 31st (d) 34th
  15. 15.What is the sum of the first 6 terms of the AP 5, 9, 13, …? (a) 25 (b) 102 (c) 180 (d) 90
  16. 16.What is the sum of all the whole numbers from 1 to 84? (a) 3570 (b) 3486 (c) 3528 (d) 7140
  17. 17.What is the 36th term of the AP 7, 15, 23, 31, …? (a) 295 (b) 288 (c) 287 (d) 280
  18. 18.What is the 18th term of the AP 19, 25, 31, 37, …? (a) 127 (b) 121 (c) 108 (d) 102
  19. 19.What is the missing term in the AP 3, ?, 7, 9, 11? (a) 4 (b) 5 (c) 6 (d) 7
  20. 20.What is the 25th term of the AP 15, 22, 29, 36, …? (a) 175 (b) 168 (c) 190 (d) 183
  21. 21.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 100 (b) 50 (c) 51 (d) 12
  22. 22.Which term of the AP 18, 21, 24, 27, … is 129? (a) 37th (b) 39th (c) 43rd (d) 38th
  23. 23.What is the sum of the first 6 terms of the AP 6, 9, 12, …? (a) 81 (b) 21 (c) 90 (d) 162
  24. 24.Which term of the AP 8, 13, 18, 23, … is 68? (a) 12th (b) 13th (c) 15th (d) 14th
  25. 25.What is the 10th term of the AP 11, 14, 17, 20, …? (a) 30 (b) 38 (c) 27 (d) 41
  26. 26.What is the sum of the first 10 terms of the AP 6, 10, 14, …? (a) 480 (b) 42 (c) 240 (d) 260
  27. 27.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 528 (c) 562 (d) 1122
  28. 28.What is the sum of the first 12 terms of the AP 4, 8, 12, …? (a) 624 (b) 336 (c) 48 (d) 312
  29. 29.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 24 (b) 144 (c) 272 (d) 136
  30. 30.What is the 13th term of the AP 12, 14, 16, 18, …? (a) 36 (b) 26 (c) 24 (d) 38
  31. 31.What is the 26th term of the AP 6, 15, 24, 33, …? (a) 240 (b) 225 (c) 231 (d) 234
  32. 32.What is the 24th term of the AP 2, 10, 18, 26, …? (a) 184 (b) 194 (c) 192 (d) 186
  33. 33.What is the sum of all the whole numbers from 1 to 36? (a) 648 (b) 630 (c) 1332 (d) 666
  34. 34.What is the 17th term of the AP 4, 11, 18, 25, …? (a) 123 (b) 119 (c) 116 (d) 112
  35. 35.What is the 19th term of the AP 10, 12, 14, 16, …? (a) 48 (b) 46 (c) 36 (d) 38
  36. 36.What is the 15th term of the AP 14, 19, 24, 29, …? (a) 70 (b) 84 (c) 75 (d) 89
  37. 37.What is the 11th term of the AP 10, 12, 14, 16, …? (a) 32 (b) 22 (c) 20 (d) 30
  38. 38.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 306 (c) 136 (d) 154
  39. 39.What is the 10th term of the AP 3, 11, 19, 27, …? (a) 80 (b) 83 (c) 72 (d) 75
  40. 40.What is the missing term in the AP 1, ?, 9, 13, 17? (a) 9 (b) 4 (c) 5 (d) 6

Answer key

  1. 324
  2. 140
  3. 26
  4. 21
  5. 14th
  6. 215
  7. 1485
  8. 48
  9. 210
  10. 4005
  11. 105
  12. 267
  13. 484
  14. 32nd
  15. 90
  16. 3570
  17. 287
  18. 121
  19. 5
  20. 183
  21. 50
  22. 38th
  23. 81
  24. 13th
  25. 38
  26. 240
  27. 561
  28. 312
  29. 136
  30. 36
  31. 231
  32. 186
  33. 666
  34. 116
  35. 46
  36. 84
  37. 30
  38. 153
  39. 75
  40. 5

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