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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 875 · 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 15th term of the AP 6, 14, 22, 30, …? (a) 112 (b) 118 (c) 120 (d) 126
  2. 2.What is the sum of all the whole numbers from 1 to 35? (a) 630 (b) 1260 (c) 595 (d) 631
  3. 3.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 31 (b) 190 (c) 350 (d) 175
  4. 4.What is the missing term in the AP 19, 27, 35, ?, 51? (a) 42 (b) 51 (c) 43 (d) 44
  5. 5.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 96 (b) 88 (c) 18 (d) 176
  6. 6.Which term of the AP 17, 22, 27, 32, … is 147? (a) 29th (b) 28th (c) 26th (d) 27th
  7. 7.What is the 33rd term of the AP 9, 13, 17, 21, …? (a) 132 (b) 141 (c) 128 (d) 137
  8. 8.What is the missing term in the AP 8, ?, 16, 20, 24? (a) 16 (b) 12 (c) 11 (d) 13
  9. 9.What is the 33rd term of the AP 16, 22, 28, 34, …? (a) 192 (b) 208 (c) 214 (d) 198
  10. 10.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 44 (b) 203 (c) 364 (d) 182
  11. 11.Which term of the AP 12, 17, 22, 27, … is 162? (a) 31st (b) 30th (c) 33rd (d) 32nd
  12. 12.What is the 20th term of the AP 13, 16, 19, 22, …? (a) 60 (b) 73 (c) 70 (d) 57
  13. 13.What is the sum of the first 7 terms of the AP 10, 16, 22, …? (a) 46 (b) 392 (c) 196 (d) 217
  14. 14.What is the 28th term of the AP 7, 13, 19, 25, …? (a) 169 (b) 175 (c) 162 (d) 168
  15. 15.What is the sum of the first 8 terms of the AP 2, 8, 14, …? (a) 368 (b) 44 (c) 184 (d) 208
  16. 16.What is the missing term in the AP 11, 19, ?, 35, 43? (a) 35 (b) 28 (c) 26 (d) 27
  17. 17.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 224 (b) 31 (c) 117 (d) 112
  18. 18.What is the 31st term of the AP 10, 13, 16, 19, …? (a) 103 (b) 90 (c) 100 (d) 93
  19. 19.What is the sum of all the whole numbers from 1 to 22? (a) 231 (b) 506 (c) 253 (d) 242
  20. 20.What is the 21st term of the AP 1, 4, 7, 10, …? (a) 60 (b) 64 (c) 61 (d) 63
  21. 21.What is the sum of the first 11 terms of the AP 10, 14, 18, …? (a) 352 (b) 660 (c) 50 (d) 330
  22. 22.Which term of the AP 11, 14, 17, 20, … is 122? (a) 38th (b) 39th (c) 40th (d) 37th
  23. 23.What is the 11th term of the AP 18, 25, 32, 39, …? (a) 95 (b) 70 (c) 88 (d) 77
  24. 24.What is the missing term in the AP 5, ?, 15, 20, 25? (a) 15 (b) 11 (c) 10 (d) 9
  25. 25.What is the missing term in the AP 9, ?, 25, 33, 41? (a) 18 (b) 16 (c) 25 (d) 17
  26. 26.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 160 (b) 28 (c) 80 (d) 95
  27. 27.What is the sum of the first 10 terms of the AP 10, 16, 22, …? (a) 400 (b) 64 (c) 370 (d) 740
  28. 28.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 9 (b) 8 (c) 10 (d) 12
  29. 29.What is the sum of the first 7 terms of the AP 6, 7, 8, …? (a) 63 (b) 64 (c) 12 (d) 126
  30. 30.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 140 (b) 26 (c) 70 (d) 85
  31. 31.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 162 (b) 324 (c) 30 (d) 165
  32. 32.What is the 39th term of the AP 10, 13, 16, 19, …? (a) 127 (b) 114 (c) 117 (d) 124
  33. 33.What is the 15th term of the AP 10, 15, 20, 25, …? (a) 75 (b) 70 (c) 85 (d) 80
  34. 34.What is the missing term in the AP 19, 24, ?, 34, 39? (a) 30 (b) 34 (c) 28 (d) 29
  35. 35.What is the sum of all the whole numbers from 1 to 42? (a) 903 (b) 1806 (c) 882 (d) 861
  36. 36.What is the 37th term of the AP 10, 16, 22, 28, …? (a) 216 (b) 222 (c) 226 (d) 232
  37. 37.What is the sum of the first 11 terms of the AP 3, 5, 7, …? (a) 23 (b) 286 (c) 154 (d) 143
  38. 38.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 20 (b) 150 (c) 84 (d) 75
  39. 39.What is the sum of all the whole numbers from 1 to 48? (a) 1128 (b) 2352 (c) 1176 (d) 1152
  40. 40.What is the 19th term of the AP 13, 17, 21, 25, …? (a) 89 (b) 76 (c) 72 (d) 85

Answer key

  1. 118
  2. 630
  3. 175
  4. 43
  5. 88
  6. 27th
  7. 137
  8. 12
  9. 208
  10. 182
  11. 31st
  12. 70
  13. 196
  14. 169
  15. 184
  16. 27
  17. 112
  18. 100
  19. 253
  20. 61
  21. 330
  22. 38th
  23. 88
  24. 10
  25. 17
  26. 80
  27. 370
  28. 9
  29. 63
  30. 70
  31. 162
  32. 124
  33. 80
  34. 29
  35. 903
  36. 226
  37. 143
  38. 75
  39. 1176
  40. 85

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