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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 981 · 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 35th term of the AP 2, 7, 12, 17, …? (a) 172 (b) 170 (c) 177 (d) 175
  2. 2.What is the missing term in the AP 2, ?, 14, 20, 26? (a) 9 (b) 14 (c) 7 (d) 8
  3. 3.What is the 40th term of the AP 19, 27, 35, 43, …? (a) 331 (b) 320 (c) 339 (d) 312
  4. 4.What is the sum of all the whole numbers from 1 to 22? (a) 242 (b) 231 (c) 253 (d) 506
  5. 5.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 462 (c) 41 (d) 231
  6. 6.What is the 31st term of the AP 14, 19, 24, 29, …? (a) 150 (b) 155 (c) 169 (d) 164
  7. 7.What is the sum of all the whole numbers from 1 to 55? (a) 1540 (b) 3080 (c) 1485 (d) 1541
  8. 8.What is the sum of the first 9 terms of the AP 2, 4, 6, …? (a) 18 (b) 99 (c) 180 (d) 90
  9. 9.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 121 (c) 21 (d) 132
  10. 10.What is the 16th term of the AP 13, 22, 31, 40, …? (a) 135 (b) 148 (c) 157 (d) 144
  11. 11.What is the 13th term of the AP 10, 13, 16, 19, …? (a) 36 (b) 39 (c) 49 (d) 46
  12. 12.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 90 (b) 96 (c) 13 (d) 180
  13. 13.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 198 (b) 27 (c) 187 (d) 374
  14. 14.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 120 (c) 240 (d) 225
  15. 15.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 190 (c) 361 (d) 380
  16. 16.What is the sum of all the whole numbers from 1 to 45? (a) 1035 (b) 2070 (c) 1036 (d) 990
  17. 17.What is the 21st term of the AP 9, 13, 17, 21, …? (a) 80 (b) 84 (c) 93 (d) 89
  18. 18.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 68 (b) 19 (c) 130 (d) 65
  19. 19.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 80 (b) 10 (c) 41 (d) 40
  20. 20.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 63 (b) 15 (c) 126 (d) 70
  21. 21.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 25 (c) 169 (d) 91
  22. 22.What is the sum of all the whole numbers from 1 to 23? (a) 277 (b) 276 (c) 253 (d) 552
  23. 23.What is the sum of all the whole numbers from 1 to 80? (a) 3240 (b) 3160 (c) 6480 (d) 3200
  24. 24.What is the 15th term of the AP 1, 6, 11, 16, …? (a) 70 (b) 76 (c) 75 (d) 71
  25. 25.What is the sum of the first 10 terms of the AP 7, 8, 9, …? (a) 115 (b) 16 (c) 120 (d) 230
  26. 26.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 726 (b) 396 (c) 363 (d) 63
  27. 27.Which term of the AP 18, 20, 22, 24, … is 68? (a) 27th (b) 34th (c) 26th (d) 25th
  28. 28.What is the missing term in the AP 6, 10, 14, ?, 22? (a) 22 (b) 19 (c) 17 (d) 18
  29. 29.Which term of the AP 14, 17, 20, 23, … is 38? (a) 8th (b) 9th (c) 11th (d) 10th
  30. 30.What is the missing term in the AP 13, ?, 27, 34, 41? (a) 21 (b) 20 (c) 27 (d) 19
  31. 31.Which term of the AP 9, 18, 27, 36, … is 81? (a) 10th (b) 11th (c) 9th (d) 8th
  32. 32.What is the missing term in the AP 1, ?, 17, 25, 33? (a) 9 (b) 8 (c) 10 (d) 17
  33. 33.What is the 25th term of the AP 15, 20, 25, 30, …? (a) 120 (b) 140 (c) 135 (d) 125
  34. 34.What is the sum of the first 10 terms of the AP 8, 11, 14, …? (a) 430 (b) 230 (c) 35 (d) 215
  35. 35.What is the missing term in the AP 8, 16, ?, 32, 40? (a) 32 (b) 25 (c) 23 (d) 24
  36. 36.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 35 (b) 60 (c) 30 (d) 10
  37. 37.What is the missing term in the AP 13, 19, ?, 31, 37? (a) 31 (b) 26 (c) 24 (d) 25
  38. 38.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 36 (c) 21 (d) 42
  39. 39.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 59 (c) 900 (d) 465
  40. 40.What is the sum of all the whole numbers from 1 to 44? (a) 990 (b) 968 (c) 946 (d) 1980

Answer key

  1. 172
  2. 8
  3. 331
  4. 253
  5. 441
  6. 164
  7. 1540
  8. 90
  9. 121
  10. 148
  11. 46
  12. 90
  13. 187
  14. 225
  15. 361
  16. 1035
  17. 89
  18. 65
  19. 40
  20. 63
  21. 169
  22. 276
  23. 3240
  24. 71
  25. 115
  26. 363
  27. 26th
  28. 18
  29. 9th
  30. 20
  31. 9th
  32. 9
  33. 135
  34. 215
  35. 24
  36. 30
  37. 25
  38. 36
  39. 900
  40. 990

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