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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 775 · 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 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 132 (c) 21 (d) 66
  2. 2.What is the sum of the first 9 terms of the AP 1, 4, 7, …? (a) 120 (b) 25 (c) 234 (d) 117
  3. 3.What is the 15th term of the AP 2, 7, 12, 17, …? (a) 72 (b) 75 (c) 77 (d) 70
  4. 4.What is the 36th term of the AP 14, 18, 22, 26, …? (a) 158 (b) 144 (c) 140 (d) 154
  5. 5.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 121 (b) 16 (c) 122 (d) 242
  6. 6.What is the 26th term of the AP 6, 12, 18, 24, …? (a) 157 (b) 150 (c) 156 (d) 162
  7. 7.What is the 16th term of the AP 20, 28, 36, 44, …? (a) 148 (b) 140 (c) 128 (d) 120
  8. 8.Which term of the AP 11, 17, 23, 29, … is 83? (a) 12th (b) 13th (c) 15th (d) 14th
  9. 9.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 84 (b) 144 (c) 72 (d) 22
  10. 10.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 9 (d) 25
  11. 11.What is the missing term in the AP 5, 12, ?, 26, 33? (a) 18 (b) 19 (c) 26 (d) 20
  12. 12.What is the 13th term of the AP 5, 13, 21, 29, …? (a) 96 (b) 104 (c) 109 (d) 101
  13. 13.What is the sum of all the whole numbers from 1 to 14? (a) 105 (b) 98 (c) 91 (d) 210
  14. 14.What is the missing term in the AP 14, 20, ?, 32, 38? (a) 26 (b) 32 (c) 27 (d) 25
  15. 15.What is the missing term in the AP 20, 26, ?, 38, 44? (a) 31 (b) 33 (c) 38 (d) 32
  16. 16.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 9 (b) 50 (c) 30 (d) 25
  17. 17.What is the 36th term of the AP 15, 20, 25, 30, …? (a) 175 (b) 195 (c) 180 (d) 190
  18. 18.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 182 (b) 44 (c) 203 (d) 364
  19. 19.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 702 (c) 51 (d) 676
  20. 20.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 27 (b) 30 (c) 54 (d) 7
  21. 21.What is the 19th term of the AP 9, 15, 21, 27, …? (a) 114 (b) 123 (c) 117 (d) 108
  22. 22.What is the missing term in the AP 8, 12, ?, 20, 24? (a) 15 (b) 20 (c) 17 (d) 16
  23. 23.What is the missing term in the AP 4, ?, 20, 28, 36? (a) 11 (b) 20 (c) 12 (d) 13
  24. 24.Which term of the AP 3, 7, 11, 15, … is 103? (a) 28th (b) 27th (c) 25th (d) 26th
  25. 25.What is the 27th term of the AP 13, 16, 19, 22, …? (a) 94 (b) 78 (c) 81 (d) 91
  26. 26.What is the sum of all the whole numbers from 1 to 48? (a) 1152 (b) 1128 (c) 2352 (d) 1176
  27. 27.What is the sum of the first 7 terms of the AP 4, 6, 8, …? (a) 77 (b) 70 (c) 140 (d) 16
  28. 28.Which term of the AP 11, 20, 29, 38, … is 182? (a) 20th (b) 22nd (c) 19th (d) 21st
  29. 29.What is the sum of the first 11 terms of the AP 1, 4, 7, …? (a) 31 (b) 352 (c) 179 (d) 176
  30. 30.What is the sum of the first 6 terms of the AP 9, 13, 17, …? (a) 114 (b) 228 (c) 29 (d) 126
  31. 31.Which term of the AP 10, 15, 20, 25, … is 200? (a) 41st (b) 39th (c) 38th (d) 40th
  32. 32.Which term of the AP 12, 18, 24, 30, … is 96? (a) 15th (b) 17th (c) 16th (d) 14th
  33. 33.What is the sum of all the whole numbers from 1 to 61? (a) 1830 (b) 3782 (c) 1892 (d) 1891
  34. 34.What is the sum of all the whole numbers from 1 to 20? (a) 200 (b) 420 (c) 210 (d) 190
  35. 35.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 171 (c) 35 (d) 324
  36. 36.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 28 (b) 145 (c) 290 (d) 160
  37. 37.What is the missing term in the AP 10, 18, ?, 34, 42? (a) 26 (b) 34 (c) 25 (d) 27
  38. 38.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 812 (c) 784 (d) 406
  39. 39.What is the missing term in the AP 6, ?, 24, 33, 42? (a) 14 (b) 16 (c) 15 (d) 24
  40. 40.What is the sum of all the whole numbers from 1 to 53? (a) 1431 (b) 1432 (c) 1378 (d) 2862

Answer key

  1. 121
  2. 117
  3. 72
  4. 154
  5. 121
  6. 156
  7. 140
  8. 13th
  9. 72
  10. 25
  11. 19
  12. 101
  13. 105
  14. 26
  15. 32
  16. 25
  17. 190
  18. 182
  19. 676
  20. 27
  21. 117
  22. 16
  23. 12
  24. 26th
  25. 91
  26. 1176
  27. 70
  28. 20th
  29. 176
  30. 114
  31. 39th
  32. 15th
  33. 1891
  34. 210
  35. 324
  36. 145
  37. 26
  38. 784
  39. 15
  40. 1431

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