← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 979 · 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 35th term of the AP 15, 23, 31, 39, …? (a) 287 (b) 295 (c) 272 (d) 280
  2. 2.Which term of the AP 17, 25, 33, 41, … is 297? (a) 38th (b) 35th (c) 36th (d) 37th
  3. 3.What is the 23rd term of the AP 11, 13, 15, 17, …? (a) 44 (b) 57 (c) 46 (d) 55
  4. 4.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 12 (b) 150 (c) 75 (d) 80
  5. 5.What is the sum of all the whole numbers from 1 to 93? (a) 4278 (b) 4372 (c) 8742 (d) 4371
  6. 6.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 400 (c) 39 (d) 210
  7. 7.Which term of the AP 5, 9, 13, 17, … is 161? (a) 40th (b) 42nd (c) 39th (d) 41st
  8. 8.What is the 30th term of the AP 9, 15, 21, 27, …? (a) 183 (b) 189 (c) 174 (d) 180
  9. 9.What is the 31st term of the AP 16, 19, 22, 25, …? (a) 106 (b) 90 (c) 93 (d) 109
  10. 10.What is the sum of the first 12 terms of the AP 10, 14, 18, …? (a) 408 (b) 768 (c) 54 (d) 384
  11. 11.What is the sum of all the whole numbers from 1 to 74? (a) 2775 (b) 5550 (c) 2738 (d) 2701
  12. 12.Which term of the AP 1, 5, 9, 13, … is 89? (a) 22nd (b) 23rd (c) 25th (d) 24th
  13. 13.What is the 30th term of the AP 1, 8, 15, 22, …? (a) 210 (b) 203 (c) 204 (d) 211
  14. 14.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 506 (b) 275 (c) 43 (d) 253
  15. 15.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 230 (b) 210 (c) 420 (d) 39
  16. 16.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 21 (c) 42 (d) 11
  17. 17.What is the sum of all the whole numbers from 1 to 13? (a) 91 (b) 92 (c) 182 (d) 78
  18. 18.What is the missing term in the AP 5, 7, 9, ?, 13? (a) 11 (b) 10 (c) 12 (d) 13
  19. 19.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 441 (c) 231 (d) 41
  20. 20.What is the 14th term of the AP 16, 23, 30, 37, …? (a) 91 (b) 107 (c) 98 (d) 114
  21. 21.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 38 (b) 13 (c) 35 (d) 70
  22. 22.Which term of the AP 8, 14, 20, 26, … is 116? (a) 19th (b) 21st (c) 20th (d) 18th
  23. 23.What is the sum of the first 11 terms of the AP 2, 5, 8, …? (a) 190 (b) 187 (c) 374 (d) 32
  24. 24.What is the sum of all the whole numbers from 1 to 49? (a) 1225 (b) 1176 (c) 1226 (d) 2450
  25. 25.What is the 17th term of the AP 18, 22, 26, 30, …? (a) 64 (b) 86 (c) 82 (d) 68
  26. 26.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 65 (b) 17 (c) 70 (d) 130
  27. 27.Which term of the AP 6, 8, 10, 12, … is 38? (a) 19th (b) 17th (c) 16th (d) 18th
  28. 28.What is the 20th term of the AP 8, 17, 26, 35, …? (a) 171 (b) 180 (c) 179 (d) 188
  29. 29.What is the 34th term of the AP 2, 5, 8, 11, …? (a) 99 (b) 104 (c) 102 (d) 101
  30. 30.What is the sum of the first 12 terms of the AP 6, 9, 12, …? (a) 39 (b) 270 (c) 540 (d) 288
  31. 31.What is the 36th term of the AP 16, 19, 22, 25, …? (a) 121 (b) 105 (c) 108 (d) 124
  32. 32.What is the sum of the first 12 terms of the AP 5, 10, 15, …? (a) 780 (b) 390 (c) 60 (d) 420
  33. 33.What is the sum of all the whole numbers from 1 to 38? (a) 1482 (b) 722 (c) 741 (d) 703
  34. 34.What is the missing term in the AP 12, ?, 22, 27, 32? (a) 22 (b) 18 (c) 17 (d) 16
  35. 35.What is the 33rd term of the AP 9, 14, 19, 24, …? (a) 160 (b) 165 (c) 169 (d) 174
  36. 36.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 30 (b) 144 (c) 256 (d) 128
  37. 37.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 246 (b) 33 (c) 138 (d) 123
  38. 38.What is the sum of all the whole numbers from 1 to 47? (a) 1081 (b) 2256 (c) 1129 (d) 1128
  39. 39.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 75 (b) 70 (c) 24 (d) 140
  40. 40.What is the 37th term of the AP 12, 21, 30, 39, …? (a) 324 (b) 345 (c) 333 (d) 336

Answer key

  1. 287
  2. 36th
  3. 55
  4. 75
  5. 4371
  6. 400
  7. 40th
  8. 183
  9. 106
  10. 384
  11. 2775
  12. 23rd
  13. 204
  14. 253
  15. 210
  16. 36
  17. 91
  18. 11
  19. 441
  20. 107
  21. 35
  22. 19th
  23. 187
  24. 1225
  25. 82
  26. 65
  27. 17th
  28. 179
  29. 101
  30. 270
  31. 121
  32. 390
  33. 741
  34. 17
  35. 169
  36. 128
  37. 123
  38. 1128
  39. 70
  40. 336

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad