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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 924 · 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 5 terms of the AP 7, 8, 9, …? (a) 90 (b) 11 (c) 46 (d) 45
  2. 2.What is the sum of the first 8 terms of the AP 5, 10, 15, …? (a) 360 (b) 180 (c) 40 (d) 200
  3. 3.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 272 (c) 256 (d) 31
  4. 4.What is the 35th term of the AP 5, 10, 15, 20, …? (a) 180 (b) 170 (c) 176 (d) 175
  5. 5.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 25 (d) 30
  6. 6.What is the missing term in the AP 16, ?, 30, 37, 44? (a) 30 (b) 24 (c) 23 (d) 22
  7. 7.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 57 (c) 841 (d) 435
  8. 8.What is the 16th term of the AP 11, 14, 17, 20, …? (a) 48 (b) 45 (c) 56 (d) 59
  9. 9.What is the 12th term of the AP 10, 13, 16, 19, …? (a) 46 (b) 33 (c) 36 (d) 43
  10. 10.Which term of the AP 5, 7, 9, 11, … is 73? (a) 37th (b) 35th (c) 34th (d) 36th
  11. 11.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 25 (c) 182 (d) 169
  12. 12.What is the missing term in the AP 7, 9, ?, 13, 15? (a) 10 (b) 13 (c) 11 (d) 12
  13. 13.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 352 (b) 385 (c) 62 (d) 704
  14. 14.What is the 10th term of the AP 13, 21, 29, 37, …? (a) 93 (b) 80 (c) 85 (d) 72
  15. 15.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 276 (c) 552 (d) 45
  16. 16.What is the 40th term of the AP 14, 19, 24, 29, …? (a) 195 (b) 209 (c) 200 (d) 214
  17. 17.What is the missing term in the AP 20, 29, ?, 47, 56? (a) 38 (b) 39 (c) 37 (d) 47
  18. 18.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 4656 (c) 4753 (d) 9506
  19. 19.What is the sum of all the whole numbers from 1 to 70? (a) 2415 (b) 2485 (c) 2450 (d) 4970
  20. 20.What is the missing term in the AP 5, 9, 13, ?, 21? (a) 17 (b) 21 (c) 18 (d) 16
  21. 21.What is the 37th term of the AP 1, 5, 9, 13, …? (a) 144 (b) 145 (c) 148 (d) 149
  22. 22.What is the 38th term of the AP 13, 15, 17, 19, …? (a) 76 (b) 89 (c) 74 (d) 87
  23. 23.Which term of the AP 12, 15, 18, 21, … is 42? (a) 10th (b) 12th (c) 11th (d) 14th
  24. 24.What is the 25th term of the AP 4, 6, 8, 10, …? (a) 50 (b) 48 (c) 52 (d) 54
  25. 25.What is the 35th term of the AP 1, 9, 17, 25, …? (a) 272 (b) 280 (c) 281 (d) 273
  26. 26.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 42 (b) 48 (c) 84 (d) 12
  27. 27.What is the missing term in the AP 11, ?, 19, 23, 27? (a) 15 (b) 16 (c) 14 (d) 19
  28. 28.What is the 28th term of the AP 3, 12, 21, 30, …? (a) 246 (b) 255 (c) 252 (d) 243
  29. 29.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 85 (b) 170 (c) 100 (d) 29
  30. 30.What is the sum of all the whole numbers from 1 to 41? (a) 861 (b) 820 (c) 1722 (d) 862
  31. 31.What is the sum of the first 9 terms of the AP 5, 11, 17, …? (a) 288 (b) 53 (c) 522 (d) 261
  32. 32.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 51 (c) 702 (d) 676
  33. 33.Which term of the AP 14, 21, 28, 35, … is 210? (a) 31st (b) 29th (c) 28th (d) 30th
  34. 34.What is the 25th term of the AP 11, 19, 27, 35, …? (a) 192 (b) 211 (c) 203 (d) 200
  35. 35.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 342 (c) 35 (d) 324
  36. 36.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 19 (c) 100 (d) 55
  37. 37.What is the missing term in the AP 5, 9, ?, 17, 21? (a) 12 (b) 17 (c) 13 (d) 14
  38. 38.What is the sum of all the whole numbers from 1 to 54? (a) 1458 (b) 1431 (c) 2970 (d) 1485
  39. 39.Which term of the AP 15, 20, 25, 30, … is 100? (a) 17th (b) 18th (c) 19th (d) 20th
  40. 40.What is the missing term in the AP 11, ?, 17, 20, 23? (a) 14 (b) 15 (c) 13 (d) 17

Answer key

  1. 45
  2. 180
  3. 256
  4. 175
  5. 25
  6. 23
  7. 841
  8. 56
  9. 43
  10. 35th
  11. 169
  12. 11
  13. 352
  14. 85
  15. 529
  16. 209
  17. 38
  18. 4753
  19. 2485
  20. 17
  21. 145
  22. 87
  23. 11th
  24. 52
  25. 273
  26. 42
  27. 15
  28. 246
  29. 85
  30. 861
  31. 261
  32. 676
  33. 29th
  34. 203
  35. 324
  36. 100
  37. 13
  38. 1485
  39. 18th
  40. 14

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