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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 945 · 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 44? (a) 946 (b) 1980 (c) 990 (d) 968
  2. 2.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 120 (b) 108 (c) 216 (d) 24
  3. 3.What is the sum of all the whole numbers from 1 to 20? (a) 190 (b) 210 (c) 200 (d) 420
  4. 4.What is the missing term in the AP 11, 13, ?, 17, 19? (a) 15 (b) 16 (c) 17 (d) 14
  5. 5.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 231 (c) 441 (d) 41
  6. 6.What is the sum of the first 12 terms of the AP 9, 12, 15, …? (a) 42 (b) 324 (c) 306 (d) 612
  7. 7.What is the 10th term of the AP 7, 10, 13, 16, …? (a) 27 (b) 30 (c) 34 (d) 37
  8. 8.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 75 (b) 80 (c) 150 (d) 12
  9. 9.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 91 (b) 182 (c) 16 (d) 92
  10. 10.What is the sum of all the whole numbers from 1 to 76? (a) 2888 (b) 2926 (c) 5852 (d) 2850
  11. 11.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 600 (d) 576
  12. 12.What is the missing term in the AP 10, 19, ?, 37, 46? (a) 28 (b) 27 (c) 37 (d) 29
  13. 13.What is the sum of the first 12 terms of the AP 7, 11, 15, …? (a) 696 (b) 372 (c) 51 (d) 348
  14. 14.What is the 30th term of the AP 13, 22, 31, 40, …? (a) 283 (b) 274 (c) 270 (d) 261
  15. 15.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 14 (b) 108 (c) 60 (d) 54
  16. 16.What is the sum of the first 9 terms of the AP 5, 6, 7, …? (a) 81 (b) 162 (c) 82 (d) 13
  17. 17.What is the missing term in the AP 15, ?, 25, 30, 35? (a) 21 (b) 20 (c) 19 (d) 25
  18. 18.What is the sum of all the whole numbers from 1 to 54? (a) 2970 (b) 1458 (c) 1485 (d) 1431
  19. 19.What is the sum of the first 9 terms of the AP 5, 8, 11, …? (a) 29 (b) 306 (c) 156 (d) 153
  20. 20.Which term of the AP 6, 12, 18, 24, … is 114? (a) 18th (b) 20th (c) 19th (d) 21st
  21. 21.What is the sum of all the whole numbers from 1 to 71? (a) 5112 (b) 2485 (c) 2556 (d) 2557
  22. 22.What is the missing term in the AP 4, 6, ?, 10, 12? (a) 10 (b) 8 (c) 7 (d) 9
  23. 23.What is the 18th term of the AP 9, 13, 17, 21, …? (a) 72 (b) 81 (c) 77 (d) 68
  24. 24.Which term of the AP 13, 20, 27, 34, … is 237? (a) 33rd (b) 32nd (c) 34th (d) 35th
  25. 25.What is the missing term in the AP 5, 12, 19, ?, 33? (a) 27 (b) 33 (c) 25 (d) 26
  26. 26.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 14 (b) 80 (c) 40 (d) 43
  27. 27.What is the sum of the first 8 terms of the AP 7, 12, 17, …? (a) 216 (b) 42 (c) 392 (d) 196
  28. 28.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 42 (c) 36 (d) 11
  29. 29.What is the 32nd term of the AP 3, 8, 13, 18, …? (a) 160 (b) 155 (c) 158 (d) 163
  30. 30.What is the sum of all the whole numbers from 1 to 53? (a) 1378 (b) 1431 (c) 2862 (d) 1432
  31. 31.What is the 30th term of the AP 5, 7, 9, 11, …? (a) 65 (b) 60 (c) 58 (d) 63
  32. 32.What is the sum of all the whole numbers from 1 to 36? (a) 648 (b) 1332 (c) 666 (d) 630
  33. 33.What is the missing term in the AP 8, 12, ?, 20, 24? (a) 15 (b) 16 (c) 17 (d) 20
  34. 34.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 66 (c) 78 (d) 156
  35. 35.What is the 39th term of the AP 5, 12, 19, 26, …? (a) 266 (b) 271 (c) 278 (d) 273
  36. 36.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 253 (c) 43 (d) 506
  37. 37.What is the 25th term of the AP 4, 10, 16, 22, …? (a) 150 (b) 154 (c) 144 (d) 148
  38. 38.What is the sum of the first 6 terms of the AP 10, 15, 20, …? (a) 270 (b) 35 (c) 135 (d) 150
  39. 39.Which term of the AP 6, 11, 16, 21, … is 41? (a) 9th (b) 8th (c) 7th (d) 10th
  40. 40.What is the sum of the first 8 terms of the AP 7, 10, 13, …? (a) 280 (b) 152 (c) 140 (d) 28

Answer key

  1. 990
  2. 108
  3. 210
  4. 15
  5. 441
  6. 306
  7. 34
  8. 75
  9. 91
  10. 2926
  11. 576
  12. 28
  13. 348
  14. 274
  15. 54
  16. 81
  17. 20
  18. 1485
  19. 153
  20. 19th
  21. 2556
  22. 8
  23. 77
  24. 33rd
  25. 26
  26. 40
  27. 196
  28. 36
  29. 158
  30. 1431
  31. 63
  32. 666
  33. 16
  34. 78
  35. 271
  36. 484
  37. 148
  38. 135
  39. 8th
  40. 140

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