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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 552 · 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.Which term of the AP 3, 9, 15, 21, … is 87? (a) 17th (b) 15th (c) 16th (d) 14th
  2. 2.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 32 (b) 252 (c) 264 (d) 504
  3. 3.Which term of the AP 8, 13, 18, 23, … is 113? (a) 23rd (b) 21st (c) 24th (d) 22nd
  4. 4.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 138 (b) 33 (c) 123 (d) 246
  5. 5.What is the sum of the first 10 terms of the AP 5, 6, 7, …? (a) 100 (b) 95 (c) 190 (d) 14
  6. 6.Which term of the AP 17, 24, 31, 38, … is 262? (a) 37th (b) 35th (c) 36th (d) 38th
  7. 7.What is the sum of the first 7 terms of the AP 10, 14, 18, …? (a) 154 (b) 34 (c) 168 (d) 308
  8. 8.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 41 (b) 450 (c) 243 (d) 225
  9. 9.What is the 32nd term of the AP 18, 22, 26, 30, …? (a) 128 (b) 146 (c) 142 (d) 124
  10. 10.What is the missing term in the AP 15, 17, ?, 21, 23? (a) 20 (b) 19 (c) 18 (d) 21
  11. 11.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 51 (c) 351 (d) 676
  12. 12.What is the sum of the first 9 terms of the AP 4, 6, 8, …? (a) 216 (b) 20 (c) 108 (d) 117
  13. 13.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 320 (b) 160 (c) 170 (d) 25
  14. 14.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 23 (c) 78 (d) 156
  15. 15.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 342 (b) 56 (c) 684 (d) 372
  16. 16.What is the 10th term of the AP 2, 4, 6, 8, …? (a) 20 (b) 21 (c) 18 (d) 22
  17. 17.Which term of the AP 13, 15, 17, 19, … is 31? (a) 9th (b) 10th (c) 12th (d) 11th
  18. 18.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 420 (c) 210 (d) 400
  19. 19.What is the sum of the first 7 terms of the AP 5, 6, 7, …? (a) 112 (b) 56 (c) 11 (d) 57
  20. 20.What is the missing term in the AP 4, ?, 8, 10, 12? (a) 6 (b) 8 (c) 5 (d) 7
  21. 21.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 138 (b) 35 (c) 240 (d) 120
  22. 22.Which term of the AP 7, 11, 15, 19, … is 163? (a) 39th (b) 42nd (c) 41st (d) 40th
  23. 23.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 37 (c) 190 (d) 361
  24. 24.What is the 30th term of the AP 16, 25, 34, 43, …? (a) 270 (b) 261 (c) 277 (d) 286
  25. 25.What is the sum of the first 7 terms of the AP 3, 8, 13, …? (a) 252 (b) 33 (c) 131 (d) 126
  26. 26.What is the 12th term of the AP 1, 5, 9, 13, …? (a) 49 (b) 48 (c) 44 (d) 45
  27. 27.What is the 31st term of the AP 9, 14, 19, 24, …? (a) 155 (b) 164 (c) 150 (d) 159
  28. 28.What is the 18th term of the AP 3, 9, 15, 21, …? (a) 102 (b) 108 (c) 111 (d) 105
  29. 29.What is the 31st term of the AP 6, 10, 14, 18, …? (a) 130 (b) 126 (c) 120 (d) 124
  30. 30.What is the sum of all the whole numbers from 1 to 71? (a) 2485 (b) 5112 (c) 2556 (d) 2557
  31. 31.Which term of the AP 3, 11, 19, 27, … is 99? (a) 12th (b) 13th (c) 14th (d) 15th
  32. 32.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 120 (b) 60 (c) 63 (d) 18
  33. 33.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 72 (c) 15 (d) 36
  34. 34.Which term of the AP 4, 9, 14, 19, … is 69? (a) 13th (b) 14th (c) 16th (d) 15th
  35. 35.What is the missing term in the AP 15, 21, ?, 33, 39? (a) 33 (b) 26 (c) 27 (d) 28
  36. 36.What is the 19th term of the AP 19, 23, 27, 31, …? (a) 76 (b) 91 (c) 95 (d) 72
  37. 37.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 100 (b) 200 (c) 110 (d) 19
  38. 38.What is the sum of all the whole numbers from 1 to 75? (a) 2851 (b) 2775 (c) 2850 (d) 5700
  39. 39.Which term of the AP 9, 15, 21, 27, … is 51? (a) 8th (b) 10th (c) 9th (d) 7th
  40. 40.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 27 (c) 196 (d) 105

Answer key

  1. 15th
  2. 252
  3. 22nd
  4. 123
  5. 95
  6. 36th
  7. 154
  8. 225
  9. 142
  10. 19
  11. 676
  12. 108
  13. 160
  14. 144
  15. 342
  16. 20
  17. 10th
  18. 400
  19. 56
  20. 6
  21. 120
  22. 40th
  23. 361
  24. 277
  25. 126
  26. 45
  27. 159
  28. 105
  29. 126
  30. 2556
  31. 13th
  32. 60
  33. 64
  34. 14th
  35. 27
  36. 91
  37. 100
  38. 2850
  39. 8th
  40. 196

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