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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 909 · 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 83? (a) 6972 (b) 3486 (c) 3487 (d) 3403
  2. 2.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 682 (b) 56 (c) 341 (d) 346
  3. 3.What is the 10th term of the AP 14, 21, 28, 35, …? (a) 84 (b) 63 (c) 77 (d) 70
  4. 4.What is the 37th term of the AP 12, 19, 26, 33, …? (a) 259 (b) 252 (c) 264 (d) 271
  5. 5.What is the sum of the first 8 terms of the AP 7, 8, 9, …? (a) 84 (b) 168 (c) 14 (d) 88
  6. 6.What is the sum of the first 11 terms of the AP 4, 10, 16, …? (a) 748 (b) 64 (c) 407 (d) 374
  7. 7.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 240 (b) 456 (c) 228 (d) 30
  8. 8.What is the 31st term of the AP 11, 17, 23, 29, …? (a) 191 (b) 180 (c) 197 (d) 186
  9. 9.What is the sum of the first 10 terms of the AP 6, 9, 12, …? (a) 210 (b) 195 (c) 390 (d) 33
  10. 10.What is the sum of all the whole numbers from 1 to 20? (a) 200 (b) 190 (c) 210 (d) 420
  11. 11.What is the missing term in the AP 15, 23, ?, 39, 47? (a) 31 (b) 30 (c) 39 (d) 32
  12. 12.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 190 (c) 361 (d) 380
  13. 13.What is the 16th term of the AP 13, 16, 19, 22, …? (a) 58 (b) 61 (c) 48 (d) 45
  14. 14.What is the missing term in the AP 5, ?, 9, 11, 13? (a) 6 (b) 7 (c) 9 (d) 8
  15. 15.What is the sum of all the whole numbers from 1 to 49? (a) 1176 (b) 2450 (c) 1225 (d) 1226
  16. 16.What is the sum of all the whole numbers from 1 to 44? (a) 990 (b) 1980 (c) 946 (d) 968
  17. 17.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 400 (c) 210 (d) 420
  18. 18.What is the sum of the first 7 terms of the AP 9, 11, 13, …? (a) 21 (b) 210 (c) 105 (d) 112
  19. 19.What is the 11th term of the AP 11, 17, 23, 29, …? (a) 60 (b) 71 (c) 77 (d) 66
  20. 20.What is the missing term in the AP 10, 16, 22, ?, 34? (a) 29 (b) 27 (c) 34 (d) 28
  21. 21.What is the 32nd term of the AP 9, 17, 25, 33, …? (a) 256 (b) 257 (c) 265 (d) 248
  22. 22.What is the sum of all the whole numbers from 1 to 53? (a) 2862 (b) 1378 (c) 1431 (d) 1432
  23. 23.What is the 12th term of the AP 13, 15, 17, 19, …? (a) 24 (b) 35 (c) 22 (d) 37
  24. 24.What is the sum of all the whole numbers from 1 to 57? (a) 3306 (b) 1596 (c) 1653 (d) 1654
  25. 25.What is the missing term in the AP 6, 10, 14, ?, 22? (a) 18 (b) 17 (c) 22 (d) 19
  26. 26.Which term of the AP 1, 6, 11, 16, … is 71? (a) 15th (b) 17th (c) 16th (d) 14th
  27. 27.What is the missing term in the AP 11, 16, 21, ?, 31? (a) 27 (b) 25 (c) 31 (d) 26
  28. 28.What is the 34th term of the AP 1, 7, 13, 19, …? (a) 205 (b) 199 (c) 198 (d) 204
  29. 29.What is the sum of the first 11 terms of the AP 4, 6, 8, …? (a) 308 (b) 24 (c) 154 (d) 165
  30. 30.What is the sum of all the whole numbers from 1 to 37? (a) 704 (b) 666 (c) 1406 (d) 703
  31. 31.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 484 (c) 506 (d) 253
  32. 32.What is the 22nd term of the AP 7, 12, 17, 22, …? (a) 105 (b) 110 (c) 112 (d) 117
  33. 33.What is the sum of all the whole numbers from 1 to 24? (a) 600 (b) 300 (c) 288 (d) 276
  34. 34.Which term of the AP 6, 8, 10, 12, … is 34? (a) 15th (b) 14th (c) 16th (d) 17th
  35. 35.What is the sum of all the whole numbers from 1 to 98? (a) 4851 (b) 9702 (c) 4753 (d) 4802
  36. 36.What is the 26th term of the AP 6, 12, 18, 24, …? (a) 162 (b) 156 (c) 157 (d) 150
  37. 37.What is the 13th term of the AP 2, 8, 14, 20, …? (a) 74 (b) 72 (c) 80 (d) 78
  38. 38.What is the 15th term of the AP 12, 18, 24, 30, …? (a) 90 (b) 102 (c) 84 (d) 96
  39. 39.What is the sum of all the whole numbers from 1 to 29? (a) 435 (b) 870 (c) 406 (d) 436
  40. 40.What is the missing term in the AP 6, 8, 10, ?, 14? (a) 14 (b) 12 (c) 11 (d) 13

Answer key

  1. 3486
  2. 341
  3. 77
  4. 264
  5. 84
  6. 374
  7. 228
  8. 191
  9. 195
  10. 210
  11. 31
  12. 361
  13. 58
  14. 7
  15. 1225
  16. 990
  17. 400
  18. 105
  19. 71
  20. 28
  21. 257
  22. 1431
  23. 35
  24. 1653
  25. 18
  26. 15th
  27. 26
  28. 199
  29. 154
  30. 703
  31. 484
  32. 112
  33. 300
  34. 15th
  35. 4851
  36. 156
  37. 74
  38. 96
  39. 435
  40. 12

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