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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 933 · 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 the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 400 (c) 39 (d) 420
  2. 2.Which term of the AP 6, 9, 12, 15, … is 75? (a) 23rd (b) 25th (c) 24th (d) 26th
  3. 3.What is the 33rd term of the AP 2, 4, 6, 8, …? (a) 67 (b) 64 (c) 66 (d) 68
  4. 4.What is the missing term in the AP 17, 26, 35, ?, 53? (a) 43 (b) 53 (c) 44 (d) 45
  5. 5.What is the 34th term of the AP 12, 21, 30, 39, …? (a) 297 (b) 309 (c) 318 (d) 306
  6. 6.What is the 33rd term of the AP 15, 22, 29, 36, …? (a) 231 (b) 246 (c) 224 (d) 239
  7. 7.What is the sum of all the whole numbers from 1 to 55? (a) 1541 (b) 1540 (c) 3080 (d) 1485
  8. 8.What is the 27th term of the AP 16, 20, 24, 28, …? (a) 124 (b) 108 (c) 104 (d) 120
  9. 9.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 19 (b) 104 (c) 96 (d) 192
  10. 10.What is the missing term in the AP 14, 20, 26, ?, 38? (a) 33 (b) 38 (c) 31 (d) 32
  11. 11.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 552 (c) 45 (d) 529
  12. 12.What is the missing term in the AP 20, 29, 38, ?, 56? (a) 48 (b) 47 (c) 46 (d) 56
  13. 13.What is the sum of all the whole numbers from 1 to 83? (a) 3403 (b) 6972 (c) 3487 (d) 3486
  14. 14.Which term of the AP 6, 11, 16, 21, … is 116? (a) 22nd (b) 24th (c) 25th (d) 23rd
  15. 15.What is the missing term in the AP 18, 26, 34, ?, 50? (a) 41 (b) 43 (c) 42 (d) 50
  16. 16.What is the sum of all the whole numbers from 1 to 10? (a) 110 (b) 45 (c) 55 (d) 50
  17. 17.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 171 (c) 380 (d) 190
  18. 18.What is the sum of all the whole numbers from 1 to 30? (a) 465 (b) 435 (c) 450 (d) 930
  19. 19.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 470 (b) 235 (c) 260 (d) 46
  20. 20.What is the missing term in the AP 11, 14, 17, ?, 23? (a) 23 (b) 20 (c) 21 (d) 19
  21. 21.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 153 (c) 33 (d) 289
  22. 22.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 4422 (c) 2145 (d) 2211
  23. 23.What is the sum of all the whole numbers from 1 to 20? (a) 200 (b) 190 (c) 210 (d) 420
  24. 24.What is the 25th term of the AP 8, 10, 12, 14, …? (a) 48 (b) 56 (c) 58 (d) 50
  25. 25.What is the missing term in the AP 17, 19, ?, 23, 25? (a) 23 (b) 20 (c) 22 (d) 21
  26. 26.What is the sum of the first 5 terms of the AP 4, 8, 12, …? (a) 70 (b) 60 (c) 120 (d) 20
  27. 27.What is the sum of all the whole numbers from 1 to 43? (a) 947 (b) 946 (c) 1892 (d) 903
  28. 28.What is the missing term in the AP 2, ?, 12, 17, 22? (a) 7 (b) 8 (c) 6 (d) 12
  29. 29.What is the missing term in the AP 14, ?, 22, 26, 30? (a) 17 (b) 19 (c) 22 (d) 18
  30. 30.What is the sum of all the whole numbers from 1 to 18? (a) 162 (b) 342 (c) 171 (d) 153
  31. 31.What is the missing term in the AP 12, ?, 18, 21, 24? (a) 15 (b) 14 (c) 16 (d) 18
  32. 32.What is the 17th term of the AP 17, 26, 35, 44, …? (a) 170 (b) 153 (c) 144 (d) 161
  33. 33.Which term of the AP 14, 17, 20, 23, … is 50? (a) 14th (b) 13th (c) 15th (d) 12th
  34. 34.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 625 (c) 49 (d) 325
  35. 35.What is the 36th term of the AP 16, 25, 34, 43, …? (a) 315 (b) 340 (c) 324 (d) 331
  36. 36.Which term of the AP 14, 23, 32, 41, … is 131? (a) 14th (b) 13th (c) 16th (d) 15th
  37. 37.What is the 15th term of the AP 16, 23, 30, 37, …? (a) 121 (b) 105 (c) 114 (d) 98
  38. 38.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 121 (b) 16 (c) 122 (d) 242
  39. 39.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 378 (c) 53 (d) 729
  40. 40.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 166 (b) 322 (c) 161 (d) 38

Answer key

  1. 400
  2. 24th
  3. 66
  4. 44
  5. 309
  6. 239
  7. 1540
  8. 120
  9. 96
  10. 32
  11. 529
  12. 47
  13. 3486
  14. 23rd
  15. 42
  16. 55
  17. 190
  18. 465
  19. 235
  20. 20
  21. 289
  22. 2211
  23. 210
  24. 56
  25. 21
  26. 60
  27. 946
  28. 7
  29. 18
  30. 171
  31. 15
  32. 161
  33. 13th
  34. 625
  35. 331
  36. 14th
  37. 114
  38. 121
  39. 729
  40. 161

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