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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 686 · 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 20, 26, ?, 38, 44? (a) 31 (b) 33 (c) 32 (d) 38
  2. 2.What is the 33rd term of the AP 6, 11, 16, 21, …? (a) 171 (b) 160 (c) 166 (d) 165
  3. 3.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 39 (d) 400
  4. 4.What is the 39th term of the AP 3, 11, 19, 27, …? (a) 304 (b) 312 (c) 315 (d) 307
  5. 5.What is the 25th term of the AP 3, 5, 7, 9, …? (a) 48 (b) 53 (c) 50 (d) 51
  6. 6.What is the sum of the first 10 terms of the AP 1, 7, 13, …? (a) 280 (b) 310 (c) 560 (d) 55
  7. 7.Which term of the AP 11, 20, 29, 38, … is 182? (a) 22nd (b) 20th (c) 19th (d) 21st
  8. 8.Which term of the AP 1, 9, 17, 25, … is 297? (a) 38th (b) 40th (c) 39th (d) 37th
  9. 9.What is the sum of the first 11 terms of the AP 9, 14, 19, …? (a) 59 (b) 374 (c) 379 (d) 748
  10. 10.What is the sum of the first 8 terms of the AP 1, 6, 11, …? (a) 36 (b) 168 (c) 296 (d) 148
  11. 11.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 600 (c) 47 (d) 576
  12. 12.What is the sum of the first 7 terms of the AP 3, 8, 13, …? (a) 126 (b) 33 (c) 131 (d) 252
  13. 13.What is the sum of all the whole numbers from 1 to 67? (a) 2211 (b) 2279 (c) 4556 (d) 2278
  14. 14.What is the sum of all the whole numbers from 1 to 30? (a) 930 (b) 435 (c) 465 (d) 450
  15. 15.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 171 (c) 342 (d) 324
  16. 16.What is the 40th term of the AP 19, 24, 29, 34, …? (a) 200 (b) 195 (c) 214 (d) 219
  17. 17.What is the 19th term of the AP 4, 6, 8, 10, …? (a) 40 (b) 36 (c) 38 (d) 42
  18. 18.Which term of the AP 1, 8, 15, 22, … is 253? (a) 38th (b) 36th (c) 39th (d) 37th
  19. 19.What is the sum of the first 8 terms of the AP 9, 13, 17, …? (a) 200 (b) 184 (c) 37 (d) 368
  20. 20.What is the missing term in the AP 7, 11, ?, 19, 23? (a) 19 (b) 16 (c) 14 (d) 15
  21. 21.What is the 38th term of the AP 13, 17, 21, 25, …? (a) 165 (b) 161 (c) 148 (d) 152
  22. 22.What is the sum of all the whole numbers from 1 to 97? (a) 4656 (b) 4753 (c) 9506 (d) 4754
  23. 23.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 27 (c) 105 (d) 196
  24. 24.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 40 (b) 12 (c) 80 (d) 45
  25. 25.What is the 28th term of the AP 15, 23, 31, 39, …? (a) 239 (b) 224 (c) 216 (d) 231
  26. 26.What is the missing term in the AP 18, 27, ?, 45, 54? (a) 36 (b) 37 (c) 45 (d) 35
  27. 27.What is the sum of all the whole numbers from 1 to 20? (a) 200 (b) 420 (c) 190 (d) 210
  28. 28.What is the missing term in the AP 17, ?, 35, 44, 53? (a) 35 (b) 25 (c) 26 (d) 27
  29. 29.Which term of the AP 8, 12, 16, 20, … is 116? (a) 28th (b) 29th (c) 27th (d) 30th
  30. 30.What is the 10th term of the AP 14, 16, 18, 20, …? (a) 18 (b) 32 (c) 20 (d) 34
  31. 31.What is the 22nd term of the AP 6, 12, 18, 24, …? (a) 126 (b) 132 (c) 133 (d) 138
  32. 32.What is the 20th term of the AP 6, 14, 22, 30, …? (a) 152 (b) 158 (c) 160 (d) 166
  33. 33.What is the 10th term of the AP 14, 23, 32, 41, …? (a) 104 (b) 81 (c) 90 (d) 95
  34. 34.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 132 (b) 22 (c) 143 (d) 264
  35. 35.What is the 17th term of the AP 12, 19, 26, 33, …? (a) 131 (b) 112 (c) 124 (d) 119
  36. 36.Which term of the AP 9, 13, 17, 21, … is 149? (a) 35th (b) 37th (c) 38th (d) 36th
  37. 37.What is the 11th term of the AP 11, 17, 23, 29, …? (a) 71 (b) 66 (c) 77 (d) 60
  38. 38.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 21 (c) 132 (d) 66
  39. 39.What is the missing term in the AP 4, 10, ?, 22, 28? (a) 16 (b) 15 (c) 17 (d) 22
  40. 40.What is the 37th term of the AP 16, 22, 28, 34, …? (a) 238 (b) 222 (c) 232 (d) 216

Answer key

  1. 32
  2. 166
  3. 400
  4. 307
  5. 51
  6. 280
  7. 20th
  8. 38th
  9. 374
  10. 148
  11. 576
  12. 126
  13. 2278
  14. 465
  15. 324
  16. 214
  17. 40
  18. 37th
  19. 184
  20. 15
  21. 161
  22. 4753
  23. 196
  24. 40
  25. 231
  26. 36
  27. 210
  28. 26
  29. 28th
  30. 32
  31. 132
  32. 158
  33. 95
  34. 132
  35. 124
  36. 36th
  37. 71
  38. 121
  39. 16
  40. 232

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