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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 281 · 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 28th term of the AP 12, 20, 28, 36, …? (a) 228 (b) 236 (c) 224 (d) 216
  2. 2.What is the 26th term of the AP 7, 9, 11, 13, …? (a) 52 (b) 59 (c) 57 (d) 50
  3. 3.What is the sum of all the whole numbers from 1 to 20? (a) 420 (b) 190 (c) 200 (d) 210
  4. 4.What is the missing term in the AP 8, 13, ?, 23, 28? (a) 17 (b) 18 (c) 19 (d) 23
  5. 5.What is the 15th term of the AP 7, 12, 17, 22, …? (a) 77 (b) 70 (c) 82 (d) 75
  6. 6.What is the sum of all the whole numbers from 1 to 59? (a) 1770 (b) 3540 (c) 1711 (d) 1771
  7. 7.Which term of the AP 10, 12, 14, 16, … is 62? (a) 31st (b) 26th (c) 28th (d) 27th
  8. 8.Which term of the AP 17, 23, 29, 35, … is 155? (a) 25th (b) 23rd (c) 24th (d) 26th
  9. 9.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 841 (c) 435 (d) 57
  10. 10.What is the 23rd term of the AP 4, 6, 8, 10, …? (a) 50 (b) 48 (c) 46 (d) 44
  11. 11.What is the missing term in the AP 14, 16, ?, 20, 22? (a) 17 (b) 20 (c) 18 (d) 19
  12. 12.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 91 (c) 25 (d) 169
  13. 13.What is the missing term in the AP 19, ?, 25, 28, 31? (a) 21 (b) 25 (c) 23 (d) 22
  14. 14.Which term of the AP 15, 19, 23, 27, … is 155? (a) 35th (b) 36th (c) 37th (d) 38th
  15. 15.What is the 20th term of the AP 6, 14, 22, 30, …? (a) 158 (b) 152 (c) 166 (d) 160
  16. 16.What is the 18th term of the AP 7, 9, 11, 13, …? (a) 34 (b) 43 (c) 41 (d) 36
  17. 17.What is the sum of all the whole numbers from 1 to 33? (a) 1122 (b) 561 (c) 562 (d) 528
  18. 18.What is the 30th term of the AP 17, 20, 23, 26, …? (a) 90 (b) 87 (c) 107 (d) 104
  19. 19.What is the 15th term of the AP 20, 26, 32, 38, …? (a) 104 (b) 110 (c) 84 (d) 90
  20. 20.What is the sum of the first 12 terms of the AP 5, 11, 17, …? (a) 71 (b) 912 (c) 456 (d) 492
  21. 21.What is the sum of all the whole numbers from 1 to 30? (a) 450 (b) 435 (c) 465 (d) 930
  22. 22.What is the missing term in the AP 14, 16, 18, ?, 22? (a) 19 (b) 20 (c) 22 (d) 21
  23. 23.What is the 35th term of the AP 1, 5, 9, 13, …? (a) 141 (b) 140 (c) 137 (d) 136
  24. 24.What is the missing term in the AP 7, ?, 21, 28, 35? (a) 21 (b) 13 (c) 14 (d) 15
  25. 25.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 29 (b) 99 (c) 114 (d) 198
  26. 26.What is the 32nd term of the AP 10, 16, 22, 28, …? (a) 192 (b) 186 (c) 196 (d) 202
  27. 27.What is the 38th term of the AP 16, 19, 22, 25, …? (a) 114 (b) 111 (c) 127 (d) 130
  28. 28.What is the 40th term of the AP 6, 11, 16, 21, …? (a) 201 (b) 195 (c) 200 (d) 206
  29. 29.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 40 (b) 80 (c) 12 (d) 45
  30. 30.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 33 (b) 168 (c) 304 (d) 152
  31. 31.What is the sum of the first 11 terms of the AP 9, 12, 15, …? (a) 39 (b) 264 (c) 528 (d) 267
  32. 32.What is the 30th term of the AP 12, 18, 24, 30, …? (a) 192 (b) 174 (c) 186 (d) 180
  33. 33.What is the sum of all the whole numbers from 1 to 78? (a) 3003 (b) 6162 (c) 3081 (d) 3042
  34. 34.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 7 (b) 54 (c) 27 (d) 30
  35. 35.What is the sum of the first 6 terms of the AP 6, 9, 12, …? (a) 81 (b) 162 (c) 90 (d) 21
  36. 36.What is the 27th term of the AP 2, 7, 12, 17, …? (a) 132 (b) 135 (c) 130 (d) 137
  37. 37.Which term of the AP 18, 20, 22, 24, … is 40? (a) 12th (b) 13th (c) 11th (d) 20th
  38. 38.What is the 32nd term of the AP 13, 22, 31, 40, …? (a) 279 (b) 301 (c) 288 (d) 292
  39. 39.What is the sum of all the whole numbers from 1 to 60? (a) 3660 (b) 1770 (c) 1830 (d) 1800
  40. 40.What is the missing term in the AP 19, 26, ?, 40, 47? (a) 32 (b) 34 (c) 40 (d) 33

Answer key

  1. 228
  2. 57
  3. 210
  4. 18
  5. 77
  6. 1770
  7. 27th
  8. 24th
  9. 841
  10. 48
  11. 18
  12. 169
  13. 22
  14. 36th
  15. 158
  16. 41
  17. 561
  18. 104
  19. 104
  20. 456
  21. 465
  22. 20
  23. 137
  24. 14
  25. 99
  26. 196
  27. 127
  28. 201
  29. 40
  30. 152
  31. 264
  32. 186
  33. 3081
  34. 27
  35. 81
  36. 132
  37. 12th
  38. 292
  39. 1830
  40. 33

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