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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 107 · 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 13th term of the AP 19, 25, 31, 37, …? (a) 97 (b) 72 (c) 91 (d) 78
  2. 2.Which term of the AP 12, 20, 28, 36, … is 108? (a) 12th (b) 13th (c) 14th (d) 15th
  3. 3.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 17 (b) 78 (c) 144 (d) 72
  4. 4.Which term of the AP 6, 9, 12, 15, … is 90? (a) 28th (b) 30th (c) 31st (d) 29th
  5. 5.What is the missing term in the AP 12, 20, ?, 36, 44? (a) 36 (b) 28 (c) 29 (d) 27
  6. 6.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 9 (c) 15 (d) 25
  7. 7.What is the missing term in the AP 7, 14, 21, ?, 35? (a) 28 (b) 29 (c) 35 (d) 27
  8. 8.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 78 (c) 23 (d) 144
  9. 9.What is the missing term in the AP 9, 12, ?, 18, 21? (a) 14 (b) 18 (c) 15 (d) 16
  10. 10.What is the missing term in the AP 4, 9, ?, 19, 24? (a) 15 (b) 14 (c) 13 (d) 19
  11. 11.What is the 14th term of the AP 6, 10, 14, 18, …? (a) 62 (b) 52 (c) 58 (d) 56
  12. 12.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 462 (c) 41 (d) 441
  13. 13.What is the 15th term of the AP 7, 10, 13, 16, …? (a) 45 (b) 52 (c) 49 (d) 42
  14. 14.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 812 (c) 784 (d) 55
  15. 15.What is the sum of all the whole numbers from 1 to 81? (a) 3240 (b) 3321 (c) 6642 (d) 3322
  16. 16.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 100 (d) 110
  17. 17.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 300 (c) 47 (d) 600
  18. 18.Which term of the AP 4, 8, 12, 16, … is 152? (a) 40th (b) 37th (c) 39th (d) 38th
  19. 19.What is the 23rd term of the AP 15, 18, 21, 24, …? (a) 81 (b) 69 (c) 84 (d) 66
  20. 20.What is the 29th term of the AP 16, 23, 30, 37, …? (a) 219 (b) 212 (c) 203 (d) 196
  21. 21.What is the sum of the first 10 terms of the AP 3, 8, 13, …? (a) 48 (b) 255 (c) 280 (d) 510
  22. 22.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 2070 (c) 1035 (d) 990
  23. 23.What is the 38th term of the AP 4, 6, 8, 10, …? (a) 78 (b) 74 (c) 76 (d) 80
  24. 24.What is the 36th term of the AP 7, 12, 17, 22, …? (a) 187 (b) 180 (c) 175 (d) 182
  25. 25.Which term of the AP 6, 10, 14, 18, … is 162? (a) 40th (b) 39th (c) 42nd (d) 41st
  26. 26.What is the 27th term of the AP 7, 14, 21, 28, …? (a) 196 (b) 182 (c) 190 (d) 189
  27. 27.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 900 (c) 930 (d) 465
  28. 28.What is the missing term in the AP 11, 17, 23, ?, 35? (a) 30 (b) 28 (c) 35 (d) 29
  29. 29.What is the sum of all the whole numbers from 1 to 68? (a) 4692 (b) 2278 (c) 2312 (d) 2346
  30. 30.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 13 (b) 10 (c) 11 (d) 12
  31. 31.What is the missing term in the AP 9, ?, 17, 21, 25? (a) 14 (b) 17 (c) 13 (d) 12
  32. 32.What is the 15th term of the AP 8, 12, 16, 20, …? (a) 64 (b) 68 (c) 56 (d) 60
  33. 33.What is the sum of all the whole numbers from 1 to 74? (a) 2701 (b) 5550 (c) 2738 (d) 2775
  34. 34.What is the missing term in the AP 14, ?, 20, 23, 26? (a) 16 (b) 17 (c) 20 (d) 18
  35. 35.What is the sum of all the whole numbers from 1 to 70? (a) 2450 (b) 2485 (c) 4970 (d) 2415
  36. 36.What is the 13th term of the AP 3, 12, 21, 30, …? (a) 120 (b) 117 (c) 108 (d) 111
  37. 37.What is the sum of all the whole numbers from 1 to 53? (a) 1431 (b) 1378 (c) 2862 (d) 1432
  38. 38.What is the sum of all the whole numbers from 1 to 96? (a) 4656 (b) 9312 (c) 4608 (d) 4560
  39. 39.What is the sum of all the whole numbers from 1 to 56? (a) 1596 (b) 1568 (c) 1540 (d) 3192
  40. 40.Which term of the AP 5, 12, 19, 26, … is 54? (a) 9th (b) 10th (c) 7th (d) 8th

Answer key

  1. 91
  2. 13th
  3. 72
  4. 29th
  5. 28
  6. 25
  7. 28
  8. 144
  9. 15
  10. 14
  11. 58
  12. 441
  13. 49
  14. 784
  15. 3321
  16. 100
  17. 576
  18. 38th
  19. 81
  20. 212
  21. 255
  22. 1035
  23. 78
  24. 182
  25. 40th
  26. 189
  27. 900
  28. 29
  29. 2346
  30. 11
  31. 13
  32. 64
  33. 2775
  34. 17
  35. 2485
  36. 111
  37. 1431
  38. 4656
  39. 1596
  40. 8th

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