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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 663 · 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 missing term in the AP 16, 18, ?, 22, 24? (a) 20 (b) 21 (c) 22 (d) 19
  2. 2.What is the sum of the first 9 terms of the AP 1, 2, 3, …? (a) 46 (b) 45 (c) 90 (d) 9
  3. 3.What is the 10th term of the AP 2, 5, 8, 11, …? (a) 29 (b) 30 (c) 27 (d) 32
  4. 4.What is the missing term in the AP 1, 9, ?, 25, 33? (a) 16 (b) 17 (c) 25 (d) 18
  5. 5.What is the 17th term of the AP 19, 27, 35, 43, …? (a) 155 (b) 128 (c) 147 (d) 136
  6. 6.What is the 29th term of the AP 11, 20, 29, 38, …? (a) 263 (b) 252 (c) 261 (d) 272
  7. 7.What is the 39th term of the AP 5, 10, 15, 20, …? (a) 200 (b) 196 (c) 190 (d) 195
  8. 8.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 406 (c) 812 (d) 55
  9. 9.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 190 (c) 380 (d) 171
  10. 10.What is the sum of the first 11 terms of the AP 5, 10, 15, …? (a) 330 (b) 55 (c) 660 (d) 335
  11. 11.What is the 25th term of the AP 5, 11, 17, 23, …? (a) 144 (b) 149 (c) 150 (d) 155
  12. 12.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 256 (c) 136 (d) 31
  13. 13.Which term of the AP 12, 18, 24, 30, … is 138? (a) 24th (b) 23rd (c) 21st (d) 22nd
  14. 14.What is the sum of all the whole numbers from 1 to 20? (a) 210 (b) 420 (c) 200 (d) 190
  15. 15.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 190 (b) 110 (c) 95 (d) 31
  16. 16.What is the sum of all the whole numbers from 1 to 14? (a) 105 (b) 91 (c) 98 (d) 210
  17. 17.Which term of the AP 16, 21, 26, 31, … is 66? (a) 12th (b) 11th (c) 10th (d) 13th
  18. 18.What is the sum of the first 9 terms of the AP 10, 16, 22, …? (a) 612 (b) 333 (c) 58 (d) 306
  19. 19.What is the 11th term of the AP 7, 15, 23, 31, …? (a) 95 (b) 80 (c) 87 (d) 88
  20. 20.What is the sum of all the whole numbers from 1 to 35? (a) 1260 (b) 595 (c) 630 (d) 631
  21. 21.What is the sum of all the whole numbers from 1 to 53? (a) 2862 (b) 1378 (c) 1431 (d) 1432
  22. 22.What is the sum of all the whole numbers from 1 to 50? (a) 1225 (b) 2550 (c) 1250 (d) 1275
  23. 23.What is the 10th term of the AP 3, 6, 9, 12, …? (a) 30 (b) 27 (c) 31 (d) 33
  24. 24.What is the missing term in the AP 13, ?, 17, 19, 21? (a) 15 (b) 14 (c) 16 (d) 17
  25. 25.What is the sum of the first 10 terms of the AP 7, 13, 19, …? (a) 370 (b) 340 (c) 680 (d) 61
  26. 26.What is the sum of the first 8 terms of the AP 7, 8, 9, …? (a) 14 (b) 168 (c) 84 (d) 88
  27. 27.What is the 15th term of the AP 11, 18, 25, 32, …? (a) 98 (b) 105 (c) 109 (d) 116
  28. 28.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 216 (b) 108 (c) 120 (d) 24
  29. 29.Which term of the AP 20, 26, 32, 38, … is 236? (a) 39th (b) 37th (c) 36th (d) 38th
  30. 30.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 240 (b) 136 (c) 29 (d) 120
  31. 31.What is the sum of the first 7 terms of the AP 1, 4, 7, …? (a) 73 (b) 19 (c) 70 (d) 140
  32. 32.Which term of the AP 14, 19, 24, 29, … is 124? (a) 25th (b) 24th (c) 23rd (d) 22nd
  33. 33.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 10 (b) 108 (c) 54 (d) 55
  34. 34.What is the 26th term of the AP 3, 10, 17, 24, …? (a) 175 (b) 185 (c) 178 (d) 182
  35. 35.What is the missing term in the AP 13, 19, 25, ?, 37? (a) 37 (b) 31 (c) 30 (d) 32
  36. 36.What is the 39th term of the AP 12, 17, 22, 27, …? (a) 195 (b) 202 (c) 190 (d) 207
  37. 37.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 17 (b) 55 (c) 110 (d) 58
  38. 38.What is the missing term in the AP 9, 14, 19, ?, 29? (a) 25 (b) 29 (c) 23 (d) 24
  39. 39.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 96 (b) 88 (c) 176 (d) 18
  40. 40.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 46 (b) 572 (c) 308 (d) 286

Answer key

  1. 20
  2. 45
  3. 29
  4. 17
  5. 147
  6. 263
  7. 195
  8. 784
  9. 190
  10. 330
  11. 149
  12. 256
  13. 22nd
  14. 210
  15. 95
  16. 105
  17. 11th
  18. 306
  19. 87
  20. 630
  21. 1431
  22. 1275
  23. 30
  24. 15
  25. 340
  26. 84
  27. 109
  28. 108
  29. 37th
  30. 120
  31. 70
  32. 23rd
  33. 54
  34. 178
  35. 31
  36. 202
  37. 55
  38. 24
  39. 88
  40. 286

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