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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 717 · 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 6, 8, 10, ?, 14? (a) 12 (b) 13 (c) 14 (d) 11
  2. 2.What is the 13th term of the AP 16, 18, 20, 22, …? (a) 42 (b) 26 (c) 40 (d) 24
  3. 3.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 171 (c) 380 (d) 190
  4. 4.What is the 16th term of the AP 14, 18, 22, 26, …? (a) 60 (b) 78 (c) 64 (d) 74
  5. 5.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 380 (c) 361 (d) 37
  6. 6.What is the 11th term of the AP 13, 16, 19, 22, …? (a) 33 (b) 43 (c) 46 (d) 30
  7. 7.What is the sum of all the whole numbers from 1 to 74? (a) 5550 (b) 2701 (c) 2738 (d) 2775
  8. 8.What is the sum of all the whole numbers from 1 to 53? (a) 1378 (b) 1432 (c) 1431 (d) 2862
  9. 9.What is the missing term in the AP 19, 21, ?, 25, 27? (a) 22 (b) 24 (c) 23 (d) 25
  10. 10.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 64 (c) 15 (d) 72
  11. 11.What is the 40th term of the AP 7, 13, 19, 25, …? (a) 247 (b) 240 (c) 234 (d) 241
  12. 12.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 240 (c) 29 (d) 225
  13. 13.Which term of the AP 20, 25, 30, 35, … is 185? (a) 37th (b) 35th (c) 34th (d) 33rd
  14. 14.What is the sum of the first 10 terms of the AP 5, 10, 15, …? (a) 550 (b) 300 (c) 50 (d) 275
  15. 15.What is the 26th term of the AP 13, 21, 29, 37, …? (a) 200 (b) 208 (c) 221 (d) 213
  16. 16.Which term of the AP 2, 8, 14, 20, … is 182? (a) 31st (b) 32nd (c) 33rd (d) 30th
  17. 17.What is the 25th term of the AP 19, 28, 37, 46, …? (a) 244 (b) 216 (c) 225 (d) 235
  18. 18.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 44 (b) 48 (c) 9 (d) 88
  19. 19.What is the missing term in the AP 20, 27, ?, 41, 48? (a) 41 (b) 35 (c) 34 (d) 33
  20. 20.Which term of the AP 8, 17, 26, 35, … is 80? (a) 11th (b) 9th (c) 10th (d) 8th
  21. 21.What is the sum of all the whole numbers from 1 to 58? (a) 3422 (b) 1653 (c) 1682 (d) 1711
  22. 22.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 85 (b) 84 (c) 168 (d) 15
  23. 23.What is the sum of all the whole numbers from 1 to 43? (a) 946 (b) 947 (c) 1892 (d) 903
  24. 24.What is the 18th term of the AP 15, 23, 31, 39, …? (a) 159 (b) 144 (c) 151 (d) 136
  25. 25.What is the sum of the first 12 terms of the AP 5, 10, 15, …? (a) 390 (b) 420 (c) 60 (d) 780
  26. 26.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 171 (c) 324 (d) 342
  27. 27.What is the sum of all the whole numbers from 1 to 75? (a) 5700 (b) 2851 (c) 2775 (d) 2850
  28. 28.Which term of the AP 1, 6, 11, 16, … is 51? (a) 11th (b) 12th (c) 10th (d) 13th
  29. 29.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 121 (c) 120 (d) 240
  30. 30.What is the 11th term of the AP 4, 7, 10, 13, …? (a) 33 (b) 37 (c) 34 (d) 30
  31. 31.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 110 (c) 50 (d) 55
  32. 32.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 169 (c) 182 (d) 25
  33. 33.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 17 (c) 45 (d) 81
  34. 34.What is the sum of all the whole numbers from 1 to 34? (a) 595 (b) 1190 (c) 578 (d) 561
  35. 35.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 153 (c) 289 (d) 33
  36. 36.What is the sum of the first 8 terms of the AP 1, 3, 5, …? (a) 64 (b) 15 (c) 128 (d) 72
  37. 37.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 66 (c) 21 (d) 121
  38. 38.What is the 31st term of the AP 5, 9, 13, 17, …? (a) 120 (b) 129 (c) 125 (d) 124
  39. 39.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 26 (b) 176 (c) 352 (d) 187
  40. 40.Which term of the AP 7, 11, 15, 19, … is 99? (a) 25th (b) 24th (c) 26th (d) 23rd

Answer key

  1. 12
  2. 40
  3. 190
  4. 74
  5. 361
  6. 43
  7. 2775
  8. 1431
  9. 23
  10. 64
  11. 241
  12. 225
  13. 34th
  14. 275
  15. 213
  16. 31st
  17. 235
  18. 44
  19. 34
  20. 9th
  21. 1711
  22. 84
  23. 946
  24. 151
  25. 390
  26. 324
  27. 2850
  28. 11th
  29. 120
  30. 34
  31. 55
  32. 169
  33. 81
  34. 595
  35. 289
  36. 64
  37. 121
  38. 125
  39. 176
  40. 24th

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