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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 505 · 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.

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  1. 1.Which term of the AP 1, 3, 5, 7, … is 17? (a) 8th (b) 11th (c) 9th (d) 10th
  2. 2.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 10 (b) 108 (c) 55 (d) 54
  3. 3.Which term of the AP 17, 26, 35, 44, … is 368? (a) 39th (b) 42nd (c) 41st (d) 40th
  4. 4.What is the sum of the first 12 terms of the AP 1, 2, 3, …? (a) 12 (b) 78 (c) 84 (d) 156
  5. 5.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 361 (c) 190 (d) 380
  6. 6.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 1122 (c) 528 (d) 562
  7. 7.Which term of the AP 6, 11, 16, 21, … is 186? (a) 39th (b) 38th (c) 37th (d) 36th
  8. 8.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 130 (b) 65 (c) 25 (d) 80
  9. 9.What is the sum of the first 7 terms of the AP 1, 5, 9, …? (a) 182 (b) 105 (c) 91 (d) 25
  10. 10.What is the 34th term of the AP 7, 13, 19, 25, …? (a) 198 (b) 205 (c) 211 (d) 204
  11. 11.Which term of the AP 13, 19, 25, 31, … is 217? (a) 36th (b) 37th (c) 34th (d) 35th
  12. 12.What is the 23rd term of the AP 20, 22, 24, 26, …? (a) 44 (b) 66 (c) 46 (d) 64
  13. 13.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 31 (c) 136 (d) 256
  14. 14.What is the sum of all the whole numbers from 1 to 22? (a) 242 (b) 506 (c) 253 (d) 231
  15. 15.What is the 35th term of the AP 14, 19, 24, 29, …? (a) 189 (b) 184 (c) 175 (d) 170
  16. 16.What is the 37th term of the AP 5, 13, 21, 29, …? (a) 293 (b) 301 (c) 288 (d) 296
  17. 17.Which term of the AP 15, 20, 25, 30, … is 110? (a) 21st (b) 22nd (c) 20th (d) 19th
  18. 18.Which term of the AP 15, 24, 33, 42, … is 312? (a) 36th (b) 33rd (c) 35th (d) 34th
  19. 19.What is the 34th term of the AP 2, 7, 12, 17, …? (a) 172 (b) 167 (c) 165 (d) 170
  20. 20.What is the 39th term of the AP 7, 16, 25, 34, …? (a) 349 (b) 342 (c) 351 (d) 358
  21. 21.Which term of the AP 15, 18, 21, 24, … is 72? (a) 24th (b) 21st (c) 19th (d) 20th
  22. 22.What is the sum of the first 10 terms of the AP 10, 15, 20, …? (a) 350 (b) 55 (c) 325 (d) 650
  23. 23.What is the sum of the first 6 terms of the AP 8, 14, 20, …? (a) 38 (b) 276 (c) 138 (d) 156
  24. 24.What is the missing term in the AP 20, ?, 34, 41, 48? (a) 26 (b) 28 (c) 27 (d) 34
  25. 25.What is the 20th term of the AP 13, 22, 31, 40, …? (a) 180 (b) 184 (c) 171 (d) 193
  26. 26.What is the 27th term of the AP 10, 13, 16, 19, …? (a) 91 (b) 88 (c) 81 (d) 78
  27. 27.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 252 (b) 135 (c) 126 (d) 22
  28. 28.What is the 22nd term of the AP 16, 22, 28, 34, …? (a) 142 (b) 126 (c) 132 (d) 148
  29. 29.What is the sum of the first 7 terms of the AP 4, 5, 6, …? (a) 98 (b) 50 (c) 49 (d) 10
  30. 30.What is the missing term in the AP 1, 10, 19, ?, 37? (a) 29 (b) 28 (c) 37 (d) 27
  31. 31.What is the 18th term of the AP 15, 20, 25, 30, …? (a) 90 (b) 85 (c) 100 (d) 105
  32. 32.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 85 (b) 26 (c) 140 (d) 70
  33. 33.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 462 (b) 429 (c) 69 (d) 858
  34. 34.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 9 (b) 12 (c) 10 (d) 8
  35. 35.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 33 (b) 152 (c) 304 (d) 168
  36. 36.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 676 (c) 702 (d) 351
  37. 37.What is the 35th term of the AP 13, 20, 27, 34, …? (a) 238 (b) 245 (c) 258 (d) 251
  38. 38.What is the 17th term of the AP 10, 14, 18, 22, …? (a) 68 (b) 64 (c) 78 (d) 74
  39. 39.Which term of the AP 18, 24, 30, 36, … is 156? (a) 23rd (b) 25th (c) 26th (d) 24th
  40. 40.What is the 25th term of the AP 9, 18, 27, 36, …? (a) 234 (b) 216 (c) 226 (d) 225

Answer key

  1. 9th
  2. 54
  3. 40th
  4. 78
  5. 361
  6. 561
  7. 37th
  8. 65
  9. 91
  10. 205
  11. 35th
  12. 64
  13. 256
  14. 253
  15. 184
  16. 293
  17. 20th
  18. 34th
  19. 167
  20. 349
  21. 20th
  22. 325
  23. 138
  24. 27
  25. 184
  26. 88
  27. 126
  28. 142
  29. 49
  30. 28
  31. 100
  32. 70
  33. 429
  34. 9
  35. 152
  36. 676
  37. 251
  38. 74
  39. 24th
  40. 225

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