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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 865 · 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 missing term in the AP 10, 12, ?, 16, 18? (a) 13 (b) 15 (c) 14 (d) 16
  2. 2.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 31 (c) 272 (d) 136
  3. 3.What is the sum of the first 11 terms of the AP 7, 11, 15, …? (a) 594 (b) 297 (c) 47 (d) 319
  4. 4.What is the sum of all the whole numbers from 1 to 54? (a) 1458 (b) 1485 (c) 1431 (d) 2970
  5. 5.What is the missing term in the AP 18, 22, ?, 30, 34? (a) 25 (b) 26 (c) 30 (d) 27
  6. 6.What is the missing term in the AP 5, ?, 9, 11, 13? (a) 8 (b) 6 (c) 7 (d) 9
  7. 7.What is the missing term in the AP 17, 25, ?, 41, 49? (a) 41 (b) 34 (c) 33 (d) 32
  8. 8.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 7 (b) 28 (c) 29 (d) 56
  9. 9.What is the 36th term of the AP 3, 6, 9, 12, …? (a) 109 (b) 105 (c) 108 (d) 111
  10. 10.Which term of the AP 11, 14, 17, 20, … is 41? (a) 13th (b) 12th (c) 10th (d) 11th
  11. 11.What is the missing term in the AP 4, ?, 14, 19, 24? (a) 8 (b) 14 (c) 10 (d) 9
  12. 12.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 342 (b) 372 (c) 56 (d) 684
  13. 13.What is the 12th term of the AP 2, 9, 16, 23, …? (a) 79 (b) 84 (c) 77 (d) 86
  14. 14.What is the 27th term of the AP 6, 13, 20, 27, …? (a) 189 (b) 195 (c) 188 (d) 182
  15. 15.Which term of the AP 5, 11, 17, 23, … is 179? (a) 31st (b) 30th (c) 29th (d) 32nd
  16. 16.What is the sum of all the whole numbers from 1 to 67? (a) 2278 (b) 4556 (c) 2279 (d) 2211
  17. 17.What is the 16th term of the AP 13, 18, 23, 28, …? (a) 88 (b) 75 (c) 93 (d) 80
  18. 18.What is the sum of all the whole numbers from 1 to 31? (a) 496 (b) 497 (c) 992 (d) 465
  19. 19.What is the 13th term of the AP 20, 24, 28, 32, …? (a) 72 (b) 52 (c) 48 (d) 68
  20. 20.What is the 12th term of the AP 17, 21, 25, 29, …? (a) 44 (b) 48 (c) 65 (d) 61
  21. 21.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 162 (b) 324 (c) 26 (d) 171
  22. 22.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 420 (b) 34 (c) 228 (d) 210
  23. 23.What is the 11th term of the AP 18, 20, 22, 24, …? (a) 40 (b) 22 (c) 20 (d) 38
  24. 24.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 91 (c) 182 (d) 25
  25. 25.Which term of the AP 2, 7, 12, 17, … is 192? (a) 41st (b) 39th (c) 40th (d) 38th
  26. 26.What is the sum of all the whole numbers from 1 to 95? (a) 4561 (b) 4560 (c) 4465 (d) 9120
  27. 27.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 196 (c) 210 (d) 105
  28. 28.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 100 (b) 53 (c) 16 (d) 50
  29. 29.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 100 (c) 55 (d) 19
  30. 30.What is the 15th term of the AP 2, 4, 6, 8, …? (a) 28 (b) 32 (c) 30 (d) 31
  31. 31.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 400 (c) 39 (d) 210
  32. 32.What is the sum of the first 12 terms of the AP 7, 8, 9, …? (a) 300 (b) 156 (c) 18 (d) 150
  33. 33.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 224 (b) 21 (c) 112 (d) 120
  34. 34.Which term of the AP 15, 17, 19, 21, … is 47? (a) 17th (b) 18th (c) 19th (d) 16th
  35. 35.What is the 36th term of the AP 3, 11, 19, 27, …? (a) 291 (b) 288 (c) 280 (d) 283
  36. 36.What is the missing term in the AP 7, 10, ?, 16, 19? (a) 12 (b) 14 (c) 13 (d) 16
  37. 37.What is the sum of all the whole numbers from 1 to 84? (a) 3486 (b) 3528 (c) 3570 (d) 7140
  38. 38.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 198 (b) 100 (c) 99 (d) 15
  39. 39.What is the 17th term of the AP 1, 6, 11, 16, …? (a) 81 (b) 86 (c) 85 (d) 80
  40. 40.What is the 37th term of the AP 9, 12, 15, 18, …? (a) 108 (b) 120 (c) 117 (d) 111

Answer key

  1. 14
  2. 256
  3. 297
  4. 1485
  5. 26
  6. 7
  7. 33
  8. 28
  9. 108
  10. 11th
  11. 9
  12. 342
  13. 79
  14. 188
  15. 30th
  16. 2278
  17. 88
  18. 496
  19. 68
  20. 61
  21. 162
  22. 210
  23. 38
  24. 169
  25. 39th
  26. 4560
  27. 196
  28. 50
  29. 100
  30. 30
  31. 400
  32. 150
  33. 112
  34. 17th
  35. 283
  36. 13
  37. 3570
  38. 99
  39. 81
  40. 117

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