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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 887 · 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 18th term of the AP 1, 7, 13, 19, …? (a) 102 (b) 109 (c) 103 (d) 108
  2. 2.What is the 26th term of the AP 7, 15, 23, 31, …? (a) 208 (b) 200 (c) 207 (d) 215
  3. 3.What is the sum of the first 8 terms of the AP 8, 13, 18, …? (a) 408 (b) 204 (c) 43 (d) 224
  4. 4.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 27 (b) 114 (c) 204 (d) 102
  5. 5.What is the 20th term of the AP 10, 16, 22, 28, …? (a) 130 (b) 124 (c) 114 (d) 120
  6. 6.What is the 40th term of the AP 17, 24, 31, 38, …? (a) 280 (b) 290 (c) 297 (d) 273
  7. 7.What is the missing term in the AP 13, 15, ?, 19, 21? (a) 16 (b) 18 (c) 19 (d) 17
  8. 8.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 13 (b) 35 (c) 70 (d) 38
  9. 9.What is the sum of all the whole numbers from 1 to 51? (a) 1327 (b) 2652 (c) 1326 (d) 1275
  10. 10.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 136 (c) 153 (d) 154
  11. 11.What is the 27th term of the AP 8, 13, 18, 23, …? (a) 138 (b) 143 (c) 130 (d) 135
  12. 12.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 225 (c) 29 (d) 120
  13. 13.What is the sum of the first 10 terms of the AP 10, 15, 20, …? (a) 55 (b) 325 (c) 650 (d) 350
  14. 14.What is the 15th term of the AP 9, 15, 21, 27, …? (a) 99 (b) 93 (c) 84 (d) 90
  15. 15.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 64 (c) 36 (d) 72
  16. 16.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 110 (c) 50 (d) 55
  17. 17.What is the 34th term of the AP 9, 11, 13, 15, …? (a) 66 (b) 68 (c) 75 (d) 77
  18. 18.What is the 17th term of the AP 1, 3, 5, 7, …? (a) 34 (b) 32 (c) 33 (d) 35
  19. 19.What is the sum of all the whole numbers from 1 to 68? (a) 4692 (b) 2346 (c) 2278 (d) 2312
  20. 20.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 35 (b) 60 (c) 30 (d) 10
  21. 21.What is the sum of the first 10 terms of the AP 9, 13, 17, …? (a) 290 (b) 270 (c) 540 (d) 45
  22. 22.What is the sum of all the whole numbers from 1 to 39? (a) 780 (b) 1560 (c) 741 (d) 781
  23. 23.What is the 22nd term of the AP 13, 16, 19, 22, …? (a) 76 (b) 79 (c) 63 (d) 66
  24. 24.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 92 (b) 91 (c) 182 (d) 16
  25. 25.What is the sum of the first 12 terms of the AP 2, 4, 6, …? (a) 24 (b) 168 (c) 312 (d) 156
  26. 26.What is the sum of all the whole numbers from 1 to 26? (a) 702 (b) 325 (c) 351 (d) 338
  27. 27.What is the 14th term of the AP 2, 5, 8, 11, …? (a) 44 (b) 42 (c) 41 (d) 39
  28. 28.What is the sum of the first 10 terms of the AP 4, 8, 12, …? (a) 440 (b) 240 (c) 40 (d) 220
  29. 29.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 13 (b) 89 (c) 88 (d) 176
  30. 30.What is the missing term in the AP 2, 5, ?, 11, 14? (a) 7 (b) 9 (c) 8 (d) 11
  31. 31.What is the 11th term of the AP 8, 13, 18, 23, …? (a) 58 (b) 50 (c) 55 (d) 63
  32. 32.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 9 (d) 25
  33. 33.What is the sum of all the whole numbers from 1 to 44? (a) 1980 (b) 946 (c) 968 (d) 990
  34. 34.Which term of the AP 2, 11, 20, 29, … is 236? (a) 26th (b) 27th (c) 29th (d) 28th
  35. 35.What is the 32nd term of the AP 9, 16, 23, 30, …? (a) 217 (b) 224 (c) 233 (d) 226
  36. 36.What is the sum of the first 5 terms of the AP 8, 12, 16, …? (a) 160 (b) 90 (c) 80 (d) 24
  37. 37.What is the 21st term of the AP 5, 7, 9, 11, …? (a) 40 (b) 45 (c) 42 (d) 47
  38. 38.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 22 (b) 143 (c) 264 (d) 132
  39. 39.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 41 (c) 462 (d) 441
  40. 40.Which term of the AP 6, 15, 24, 33, … is 123? (a) 16th (b) 15th (c) 14th (d) 13th

Answer key

  1. 103
  2. 207
  3. 204
  4. 102
  5. 124
  6. 290
  7. 17
  8. 35
  9. 1326
  10. 153
  11. 138
  12. 225
  13. 325
  14. 93
  15. 64
  16. 55
  17. 75
  18. 33
  19. 2346
  20. 30
  21. 270
  22. 780
  23. 76
  24. 91
  25. 156
  26. 351
  27. 41
  28. 220
  29. 88
  30. 8
  31. 58
  32. 25
  33. 990
  34. 27th
  35. 226
  36. 80
  37. 45
  38. 132
  39. 441
  40. 14th

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