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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 263 · 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 26th term of the AP 7, 14, 21, 28, …? (a) 189 (b) 183 (c) 182 (d) 175
  2. 2.What is the sum of all the whole numbers from 1 to 39? (a) 780 (b) 781 (c) 741 (d) 1560
  3. 3.What is the missing term in the AP 16, ?, 20, 22, 24? (a) 17 (b) 20 (c) 19 (d) 18
  4. 4.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 196 (c) 105 (d) 27
  5. 5.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 75 (b) 12 (c) 80 (d) 150
  6. 6.What is the sum of the first 10 terms of the AP 6, 7, 8, …? (a) 110 (b) 15 (c) 105 (d) 210
  7. 7.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 80 (b) 20 (c) 77 (d) 154
  8. 8.What is the sum of all the whole numbers from 1 to 22? (a) 242 (b) 506 (c) 253 (d) 231
  9. 9.What is the 13th term of the AP 15, 19, 23, 27, …? (a) 48 (b) 67 (c) 63 (d) 52
  10. 10.What is the missing term in the AP 8, 13, 18, ?, 28? (a) 22 (b) 24 (c) 23 (d) 28
  11. 11.What is the sum of all the whole numbers from 1 to 75? (a) 2850 (b) 5700 (c) 2851 (d) 2775
  12. 12.Which term of the AP 4, 11, 18, 25, … is 53? (a) 9th (b) 10th (c) 8th (d) 7th
  13. 13.What is the 21st term of the AP 6, 8, 10, 12, …? (a) 40 (b) 46 (c) 48 (d) 42
  14. 14.What is the 30th term of the AP 2, 8, 14, 20, …? (a) 174 (b) 182 (c) 180 (d) 176
  15. 15.Which term of the AP 9, 18, 27, 36, … is 261? (a) 30th (b) 28th (c) 29th (d) 31st
  16. 16.What is the 14th term of the AP 4, 11, 18, 25, …? (a) 98 (b) 91 (c) 95 (d) 102
  17. 17.What is the sum of the first 8 terms of the AP 9, 12, 15, …? (a) 30 (b) 168 (c) 312 (d) 156
  18. 18.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 144 (b) 286 (c) 18 (d) 143
  19. 19.What is the 14th term of the AP 14, 20, 26, 32, …? (a) 78 (b) 84 (c) 92 (d) 98
  20. 20.What is the sum of the first 8 terms of the AP 8, 10, 12, …? (a) 240 (b) 22 (c) 120 (d) 128
  21. 21.What is the 38th term of the AP 13, 19, 25, 31, …? (a) 235 (b) 241 (c) 228 (d) 222
  22. 22.What is the 15th term of the AP 1, 3, 5, 7, …? (a) 29 (b) 31 (c) 28 (d) 30
  23. 23.What is the sum of all the whole numbers from 1 to 67? (a) 2279 (b) 2278 (c) 2211 (d) 4556
  24. 24.What is the 24th term of the AP 2, 4, 6, 8, …? (a) 50 (b) 46 (c) 49 (d) 48
  25. 25.What is the 13th term of the AP 10, 13, 16, 19, …? (a) 46 (b) 49 (c) 39 (d) 36
  26. 26.What is the sum of all the whole numbers from 1 to 52? (a) 1352 (b) 2756 (c) 1326 (d) 1378
  27. 27.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 192 (b) 372 (c) 21 (d) 186
  28. 28.What is the sum of all the whole numbers from 1 to 47? (a) 1129 (b) 1128 (c) 1081 (d) 2256
  29. 29.What is the sum of the first 5 terms of the AP 8, 13, 18, …? (a) 180 (b) 28 (c) 95 (d) 90
  30. 30.What is the 34th term of the AP 9, 18, 27, 36, …? (a) 315 (b) 297 (c) 306 (d) 307
  31. 31.What is the sum of the first 6 terms of the AP 7, 12, 17, …? (a) 117 (b) 234 (c) 32 (d) 132
  32. 32.What is the 35th term of the AP 2, 6, 10, 14, …? (a) 142 (b) 138 (c) 140 (d) 136
  33. 33.Which term of the AP 8, 13, 18, 23, … is 143? (a) 30th (b) 29th (c) 28th (d) 27th
  34. 34.What is the sum of the first 7 terms of the AP 2, 8, 14, …? (a) 38 (b) 161 (c) 280 (d) 140
  35. 35.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 228 (b) 420 (c) 210 (d) 34
  36. 36.What is the missing term in the AP 16, ?, 24, 28, 32? (a) 20 (b) 24 (c) 21 (d) 19
  37. 37.Which term of the AP 1, 10, 19, 28, … is 199? (a) 23rd (b) 24th (c) 22nd (d) 25th
  38. 38.What is the sum of all the whole numbers from 1 to 70? (a) 2450 (b) 4970 (c) 2415 (d) 2485
  39. 39.What is the 34th term of the AP 12, 15, 18, 21, …? (a) 114 (b) 99 (c) 102 (d) 111
  40. 40.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 2145 (c) 2211 (d) 4422

Answer key

  1. 182
  2. 780
  3. 18
  4. 196
  5. 75
  6. 105
  7. 77
  8. 253
  9. 63
  10. 23
  11. 2850
  12. 8th
  13. 46
  14. 176
  15. 29th
  16. 95
  17. 156
  18. 143
  19. 92
  20. 120
  21. 235
  22. 29
  23. 2278
  24. 48
  25. 46
  26. 1378
  27. 186
  28. 1128
  29. 90
  30. 306
  31. 117
  32. 138
  33. 28th
  34. 140
  35. 210
  36. 20
  37. 23rd
  38. 2485
  39. 111
  40. 2211

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