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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 896 · 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 all the whole numbers from 1 to 96? (a) 9312 (b) 4656 (c) 4560 (d) 4608
  2. 2.What is the 10th term of the AP 5, 8, 11, 14, …? (a) 35 (b) 32 (c) 27 (d) 30
  3. 3.Which term of the AP 12, 20, 28, 36, … is 252? (a) 33rd (b) 31st (c) 30th (d) 32nd
  4. 4.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 26 (b) 85 (c) 70 (d) 140
  5. 5.What is the 18th term of the AP 16, 19, 22, 25, …? (a) 67 (b) 51 (c) 70 (d) 54
  6. 6.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 110 (b) 10 (c) 55 (d) 60
  7. 7.What is the 33rd term of the AP 7, 15, 23, 31, …? (a) 271 (b) 256 (c) 263 (d) 264
  8. 8.Which term of the AP 13, 18, 23, 28, … is 53? (a) 10th (b) 8th (c) 9th (d) 11th
  9. 9.What is the missing term in the AP 3, 8, 13, ?, 23? (a) 23 (b) 19 (c) 18 (d) 17
  10. 10.What is the 38th term of the AP 1, 4, 7, 10, …? (a) 112 (b) 114 (c) 115 (d) 111
  11. 11.What is the missing term in the AP 1, 6, ?, 16, 21? (a) 12 (b) 10 (c) 11 (d) 16
  12. 12.Which term of the AP 15, 17, 19, 21, … is 53? (a) 22nd (b) 20th (c) 21st (d) 19th
  13. 13.What is the sum of all the whole numbers from 1 to 65? (a) 2146 (b) 2145 (c) 2080 (d) 4290
  14. 14.What is the sum of the first 7 terms of the AP 5, 6, 7, …? (a) 56 (b) 11 (c) 112 (d) 57
  15. 15.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 78 (c) 156 (d) 144
  16. 16.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 11 (b) 12 (c) 13 (d) 10
  17. 17.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 17 (b) 154 (c) 84 (d) 77
  18. 18.Which term of the AP 18, 27, 36, 45, … is 306? (a) 35th (b) 33rd (c) 34th (d) 32nd
  19. 19.What is the 37th term of the AP 4, 6, 8, 10, …? (a) 78 (b) 74 (c) 76 (d) 72
  20. 20.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 56 (c) 28 (d) 49
  21. 21.What is the 39th term of the AP 8, 16, 24, 32, …? (a) 304 (b) 313 (c) 320 (d) 312
  22. 22.What is the sum of the first 8 terms of the AP 7, 12, 17, …? (a) 392 (b) 42 (c) 196 (d) 216
  23. 23.Which term of the AP 2, 5, 8, 11, … is 26? (a) 9th (b) 10th (c) 8th (d) 11th
  24. 24.What is the 35th term of the AP 16, 24, 32, 40, …? (a) 296 (b) 288 (c) 280 (d) 272
  25. 25.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 306 (d) 289
  26. 26.What is the sum of the first 8 terms of the AP 7, 13, 19, …? (a) 224 (b) 448 (c) 49 (d) 248
  27. 27.What is the missing term in the AP 15, ?, 31, 39, 47? (a) 24 (b) 31 (c) 23 (d) 22
  28. 28.What is the sum of the first 7 terms of the AP 5, 8, 11, …? (a) 23 (b) 196 (c) 101 (d) 98
  29. 29.What is the 12th term of the AP 15, 24, 33, 42, …? (a) 114 (b) 99 (c) 108 (d) 123
  30. 30.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 60 (b) 120 (c) 18 (d) 63
  31. 31.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 99 (b) 108 (c) 198 (d) 19
  32. 32.What is the 35th term of the AP 17, 19, 21, 23, …? (a) 87 (b) 70 (c) 85 (d) 68
  33. 33.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 11 (b) 120 (c) 60 (d) 64
  34. 34.What is the sum of all the whole numbers from 1 to 19? (a) 171 (b) 190 (c) 191 (d) 380
  35. 35.What is the 17th term of the AP 4, 7, 10, 13, …? (a) 55 (b) 48 (c) 51 (d) 52
  36. 36.Which term of the AP 10, 19, 28, 37, … is 244? (a) 29th (b) 28th (c) 26th (d) 27th
  37. 37.What is the 32nd term of the AP 11, 19, 27, 35, …? (a) 259 (b) 267 (c) 248 (d) 256
  38. 38.What is the 22nd term of the AP 5, 11, 17, 23, …? (a) 132 (b) 137 (c) 126 (d) 131
  39. 39.What is the 10th term of the AP 4, 8, 12, 16, …? (a) 40 (b) 36 (c) 44 (d) 41
  40. 40.What is the 36th term of the AP 6, 14, 22, 30, …? (a) 280 (b) 288 (c) 294 (d) 286

Answer key

  1. 4656
  2. 32
  3. 31st
  4. 70
  5. 67
  6. 55
  7. 263
  8. 9th
  9. 18
  10. 112
  11. 11
  12. 20th
  13. 2145
  14. 56
  15. 144
  16. 11
  17. 77
  18. 33rd
  19. 76
  20. 49
  21. 312
  22. 196
  23. 9th
  24. 288
  25. 289
  26. 224
  27. 23
  28. 98
  29. 114
  30. 60
  31. 99
  32. 85
  33. 60
  34. 190
  35. 52
  36. 27th
  37. 259
  38. 131
  39. 40
  40. 286

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