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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 987 · 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 17th term of the AP 8, 15, 22, 29, …? (a) 120 (b) 127 (c) 119 (d) 112
  2. 2.What is the missing term in the AP 10, ?, 22, 28, 34? (a) 15 (b) 22 (c) 16 (d) 17
  3. 3.Which term of the AP 20, 22, 24, 26, … is 52? (a) 17th (b) 18th (c) 26th (d) 16th
  4. 4.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 92 (c) 91 (d) 78
  5. 5.What is the sum of all the whole numbers from 1 to 55? (a) 1540 (b) 3080 (c) 1485 (d) 1541
  6. 6.Which term of the AP 8, 10, 12, 14, … is 38? (a) 16th (b) 15th (c) 19th (d) 17th
  7. 7.Which term of the AP 19, 28, 37, 46, … is 109? (a) 12th (b) 13th (c) 10th (d) 11th
  8. 8.What is the sum of the first 7 terms of the AP 6, 7, 8, …? (a) 63 (b) 64 (c) 12 (d) 126
  9. 9.What is the missing term in the AP 14, ?, 30, 38, 46? (a) 21 (b) 22 (c) 23 (d) 30
  10. 10.What is the 13th term of the AP 2, 5, 8, 11, …? (a) 41 (b) 38 (c) 36 (d) 39
  11. 11.What is the sum of all the whole numbers from 1 to 52? (a) 1378 (b) 2756 (c) 1326 (d) 1352
  12. 12.What is the sum of the first 11 terms of the AP 3, 5, 7, …? (a) 286 (b) 23 (c) 154 (d) 143
  13. 13.What is the 33rd term of the AP 20, 25, 30, 35, …? (a) 160 (b) 180 (c) 185 (d) 165
  14. 14.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 552 (c) 529 (d) 45
  15. 15.What is the sum of all the whole numbers from 1 to 14? (a) 210 (b) 98 (c) 91 (d) 105
  16. 16.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 676 (c) 51 (d) 702
  17. 17.What is the 13th term of the AP 11, 15, 19, 23, …? (a) 63 (b) 48 (c) 59 (d) 52
  18. 18.What is the sum of all the whole numbers from 1 to 67? (a) 2279 (b) 2278 (c) 4556 (d) 2211
  19. 19.What is the 16th term of the AP 9, 11, 13, 15, …? (a) 30 (b) 39 (c) 41 (d) 32
  20. 20.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 182 (c) 25 (d) 169
  21. 21.Which term of the AP 12, 17, 22, 27, … is 92? (a) 16th (b) 18th (c) 19th (d) 17th
  22. 22.What is the 38th term of the AP 2, 8, 14, 20, …? (a) 230 (b) 224 (c) 228 (d) 222
  23. 23.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 96 (b) 13 (c) 90 (d) 180
  24. 24.What is the sum of the first 5 terms of the AP 9, 13, 17, …? (a) 95 (b) 170 (c) 25 (d) 85
  25. 25.Which term of the AP 18, 21, 24, 27, … is 54? (a) 12th (b) 14th (c) 18th (d) 13th
  26. 26.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 13 (b) 126 (c) 63 (d) 66
  27. 27.Which term of the AP 11, 19, 27, 35, … is 75? (a) 9th (b) 8th (c) 10th (d) 11th
  28. 28.What is the 35th term of the AP 6, 11, 16, 21, …? (a) 175 (b) 170 (c) 176 (d) 181
  29. 29.What is the sum of all the whole numbers from 1 to 10? (a) 55 (b) 45 (c) 110 (d) 50
  30. 30.What is the 37th term of the AP 14, 20, 26, 32, …? (a) 216 (b) 222 (c) 236 (d) 230
  31. 31.What is the 20th term of the AP 6, 12, 18, 24, …? (a) 121 (b) 120 (c) 126 (d) 114
  32. 32.What is the missing term in the AP 15, ?, 25, 30, 35? (a) 21 (b) 25 (c) 19 (d) 20
  33. 33.What is the 37th term of the AP 12, 19, 26, 33, …? (a) 264 (b) 252 (c) 271 (d) 259
  34. 34.What is the 15th term of the AP 17, 19, 21, 23, …? (a) 28 (b) 30 (c) 45 (d) 47
  35. 35.Which term of the AP 10, 15, 20, 25, … is 85? (a) 15th (b) 16th (c) 18th (d) 17th
  36. 36.Which term of the AP 3, 9, 15, 21, … is 81? (a) 16th (b) 15th (c) 13th (d) 14th
  37. 37.What is the missing term in the AP 4, 13, ?, 31, 40? (a) 31 (b) 22 (c) 23 (d) 21
  38. 38.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 144 (b) 256 (c) 128 (d) 30
  39. 39.What is the 15th term of the AP 11, 16, 21, 26, …? (a) 70 (b) 81 (c) 75 (d) 86
  40. 40.What is the 10th term of the AP 1, 7, 13, 19, …? (a) 55 (b) 60 (c) 54 (d) 61

Answer key

  1. 120
  2. 16
  3. 17th
  4. 91
  5. 1540
  6. 16th
  7. 11th
  8. 63
  9. 22
  10. 38
  11. 1378
  12. 143
  13. 180
  14. 529
  15. 105
  16. 676
  17. 59
  18. 2278
  19. 39
  20. 169
  21. 17th
  22. 224
  23. 90
  24. 85
  25. 13th
  26. 63
  27. 9th
  28. 176
  29. 55
  30. 230
  31. 120
  32. 20
  33. 264
  34. 45
  35. 16th
  36. 14th
  37. 22
  38. 128
  39. 81
  40. 55

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