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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 905 · 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 6 terms of the AP 5, 9, 13, …? (a) 180 (b) 102 (c) 90 (d) 25
  2. 2.What is the 19th term of the AP 17, 22, 27, 32, …? (a) 112 (b) 90 (c) 95 (d) 107
  3. 3.What is the sum of all the whole numbers from 1 to 23? (a) 276 (b) 277 (c) 253 (d) 552
  4. 4.What is the 19th term of the AP 14, 19, 24, 29, …? (a) 104 (b) 95 (c) 109 (d) 90
  5. 5.What is the sum of the first 11 terms of the AP 1, 7, 13, …? (a) 374 (b) 682 (c) 341 (d) 61
  6. 6.What is the missing term in the AP 14, 19, ?, 29, 34? (a) 25 (b) 24 (c) 29 (d) 23
  7. 7.What is the sum of all the whole numbers from 1 to 41? (a) 861 (b) 1722 (c) 820 (d) 862
  8. 8.What is the 24th term of the AP 3, 12, 21, 30, …? (a) 219 (b) 207 (c) 216 (d) 210
  9. 9.Which term of the AP 18, 25, 32, 39, … is 144? (a) 21st (b) 20th (c) 18th (d) 19th
  10. 10.What is the 32nd term of the AP 14, 23, 32, 41, …? (a) 293 (b) 302 (c) 279 (d) 288
  11. 11.What is the missing term in the AP 14, 16, ?, 20, 22? (a) 17 (b) 18 (c) 20 (d) 19
  12. 12.What is the 13th term of the AP 7, 15, 23, 31, …? (a) 96 (b) 104 (c) 103 (d) 111
  13. 13.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 153 (b) 306 (c) 33 (d) 171
  14. 14.What is the missing term in the AP 3, 10, 17, ?, 31? (a) 23 (b) 24 (c) 25 (d) 31
  15. 15.What is the sum of all the whole numbers from 1 to 30? (a) 450 (b) 435 (c) 930 (d) 465
  16. 16.What is the missing term in the AP 11, 14, 17, ?, 23? (a) 19 (b) 23 (c) 21 (d) 20
  17. 17.What is the sum of all the whole numbers from 1 to 20? (a) 190 (b) 420 (c) 200 (d) 210
  18. 18.What is the sum of the first 7 terms of the AP 5, 10, 15, …? (a) 280 (b) 35 (c) 145 (d) 140
  19. 19.What is the sum of all the whole numbers from 1 to 70? (a) 4970 (b) 2415 (c) 2450 (d) 2485
  20. 20.Which term of the AP 11, 13, 15, 17, … is 81? (a) 38th (b) 36th (c) 35th (d) 37th
  21. 21.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 225 (b) 41 (c) 450 (d) 243
  22. 22.What is the sum of the first 12 terms of the AP 9, 12, 15, …? (a) 324 (b) 612 (c) 42 (d) 306
  23. 23.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 276 (c) 529 (d) 552
  24. 24.What is the missing term in the AP 4, 12, ?, 28, 36? (a) 28 (b) 19 (c) 20 (d) 21
  25. 25.Which term of the AP 6, 9, 12, 15, … is 57? (a) 17th (b) 20th (c) 19th (d) 18th
  26. 26.What is the sum of the first 8 terms of the AP 1, 6, 11, …? (a) 36 (b) 168 (c) 148 (d) 296
  27. 27.What is the missing term in the AP 17, ?, 23, 26, 29? (a) 19 (b) 20 (c) 23 (d) 21
  28. 28.What is the missing term in the AP 15, 21, 27, ?, 39? (a) 39 (b) 34 (c) 32 (d) 33
  29. 29.What is the sum of the first 10 terms of the AP 6, 12, 18, …? (a) 60 (b) 360 (c) 660 (d) 330
  30. 30.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 729 (c) 53 (d) 756
  31. 31.What is the 31st term of the AP 12, 19, 26, 33, …? (a) 229 (b) 217 (c) 222 (d) 210
  32. 32.Which term of the AP 7, 10, 13, 16, … is 61? (a) 21st (b) 20th (c) 19th (d) 18th
  33. 33.What is the missing term in the AP 1, 6, ?, 16, 21? (a) 10 (b) 12 (c) 16 (d) 11
  34. 34.What is the sum of all the whole numbers from 1 to 73? (a) 2702 (b) 2701 (c) 5402 (d) 2628
  35. 35.What is the missing term in the AP 20, ?, 28, 32, 36? (a) 25 (b) 28 (c) 23 (d) 24
  36. 36.What is the missing term in the AP 20, ?, 24, 26, 28? (a) 24 (b) 21 (c) 22 (d) 23
  37. 37.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 364 (b) 44 (c) 182 (d) 203
  38. 38.What is the 32nd term of the AP 10, 17, 24, 31, …? (a) 224 (b) 217 (c) 227 (d) 234
  39. 39.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 126 (b) 222 (c) 31 (d) 111
  40. 40.What is the 23rd term of the AP 6, 13, 20, 27, …? (a) 154 (b) 161 (c) 160 (d) 167

Answer key

  1. 90
  2. 107
  3. 276
  4. 104
  5. 341
  6. 24
  7. 861
  8. 210
  9. 19th
  10. 293
  11. 18
  12. 103
  13. 153
  14. 24
  15. 465
  16. 20
  17. 210
  18. 140
  19. 2485
  20. 36th
  21. 225
  22. 306
  23. 529
  24. 20
  25. 18th
  26. 148
  27. 20
  28. 33
  29. 330
  30. 729
  31. 222
  32. 19th
  33. 11
  34. 2701
  35. 24
  36. 22
  37. 182
  38. 227
  39. 111
  40. 160

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