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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 293 · 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 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 272 (c) 256 (d) 31
  2. 2.What is the sum of the first 5 terms of the AP 5, 6, 7, …? (a) 70 (b) 35 (c) 36 (d) 9
  3. 3.What is the sum of all the whole numbers from 1 to 69? (a) 2415 (b) 2346 (c) 4830 (d) 2416
  4. 4.What is the 38th term of the AP 5, 10, 15, 20, …? (a) 185 (b) 195 (c) 191 (d) 190
  5. 5.What is the sum of the first 7 terms of the AP 7, 11, 15, …? (a) 133 (b) 31 (c) 147 (d) 266
  6. 6.What is the sum of all the whole numbers from 1 to 18? (a) 171 (b) 153 (c) 342 (d) 162
  7. 7.What is the sum of the first 11 terms of the AP 1, 4, 7, …? (a) 352 (b) 179 (c) 176 (d) 31
  8. 8.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 17 (c) 45 (d) 81
  9. 9.What is the missing term in the AP 15, 22, 29, ?, 43? (a) 37 (b) 35 (c) 43 (d) 36
  10. 10.What is the 15th term of the AP 1, 6, 11, 16, …? (a) 75 (b) 71 (c) 70 (d) 76
  11. 11.Which term of the AP 19, 25, 31, 37, … is 109? (a) 17th (b) 16th (c) 18th (d) 15th
  12. 12.What is the missing term in the AP 3, 5, ?, 9, 11? (a) 8 (b) 7 (c) 9 (d) 6
  13. 13.What is the 33rd term of the AP 13, 15, 17, 19, …? (a) 66 (b) 77 (c) 64 (d) 79
  14. 14.Which term of the AP 13, 16, 19, 22, … is 64? (a) 20th (b) 19th (c) 17th (d) 18th
  15. 15.Which term of the AP 11, 17, 23, 29, … is 161? (a) 25th (b) 28th (c) 26th (d) 27th
  16. 16.What is the sum of all the whole numbers from 1 to 78? (a) 3003 (b) 6162 (c) 3081 (d) 3042
  17. 17.What is the sum of all the whole numbers from 1 to 47? (a) 1081 (b) 1128 (c) 2256 (d) 1129
  18. 18.What is the missing term in the AP 2, 9, 16, ?, 30? (a) 22 (b) 30 (c) 23 (d) 24
  19. 19.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 144 (b) 24 (c) 136 (d) 272
  20. 20.What is the sum of all the whole numbers from 1 to 80? (a) 3200 (b) 3240 (c) 3160 (d) 6480
  21. 21.What is the 12th term of the AP 8, 15, 22, 29, …? (a) 77 (b) 84 (c) 85 (d) 92
  22. 22.What is the sum of all the whole numbers from 1 to 73? (a) 2628 (b) 2702 (c) 2701 (d) 5402
  23. 23.What is the sum of the first 10 terms of the AP 4, 9, 14, …? (a) 530 (b) 49 (c) 290 (d) 265
  24. 24.What is the missing term in the AP 13, 15, 17, ?, 21? (a) 18 (b) 20 (c) 21 (d) 19
  25. 25.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 49 (c) 625 (d) 325
  26. 26.What is the sum of the first 10 terms of the AP 5, 6, 7, …? (a) 100 (b) 190 (c) 14 (d) 95
  27. 27.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 53 (c) 729 (d) 378
  28. 28.What is the missing term in the AP 11, 15, ?, 23, 27? (a) 23 (b) 19 (c) 18 (d) 20
  29. 29.What is the sum of all the whole numbers from 1 to 53? (a) 1432 (b) 1378 (c) 1431 (d) 2862
  30. 30.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 210 (c) 39 (d) 420
  31. 31.What is the sum of all the whole numbers from 1 to 96? (a) 4608 (b) 9312 (c) 4560 (d) 4656
  32. 32.Which term of the AP 7, 15, 23, 31, … is 295? (a) 39th (b) 37th (c) 36th (d) 38th
  33. 33.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 27 (c) 196 (d) 105
  34. 34.What is the sum of the first 9 terms of the AP 10, 16, 22, …? (a) 612 (b) 333 (c) 306 (d) 58
  35. 35.What is the 24th term of the AP 14, 19, 24, 29, …? (a) 134 (b) 120 (c) 129 (d) 115
  36. 36.What is the 24th term of the AP 5, 8, 11, 14, …? (a) 72 (b) 77 (c) 74 (d) 69
  37. 37.What is the 35th term of the AP 11, 19, 27, 35, …? (a) 291 (b) 272 (c) 280 (d) 283
  38. 38.What is the 18th term of the AP 1, 8, 15, 22, …? (a) 126 (b) 127 (c) 120 (d) 119
  39. 39.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 72 (b) 11 (c) 36 (d) 42
  40. 40.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 153 (c) 306 (d) 33

Answer key

  1. 256
  2. 35
  3. 2415
  4. 190
  5. 133
  6. 171
  7. 176
  8. 81
  9. 36
  10. 71
  11. 16th
  12. 7
  13. 77
  14. 18th
  15. 26th
  16. 3081
  17. 1128
  18. 23
  19. 136
  20. 3240
  21. 85
  22. 2701
  23. 265
  24. 19
  25. 625
  26. 95
  27. 729
  28. 19
  29. 1431
  30. 400
  31. 4656
  32. 37th
  33. 196
  34. 306
  35. 129
  36. 74
  37. 283
  38. 120
  39. 36
  40. 289

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