← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 13 · 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 30th term of the AP 11, 19, 27, 35, …? (a) 251 (b) 232 (c) 243 (d) 240
  2. 2.Which term of the AP 18, 23, 28, 33, … is 178? (a) 35th (b) 32nd (c) 33rd (d) 34th
  3. 3.What is the 11th term of the AP 13, 20, 27, 34, …? (a) 70 (b) 77 (c) 90 (d) 83
  4. 4.What is the 28th term of the AP 2, 5, 8, 11, …? (a) 81 (b) 86 (c) 84 (d) 83
  5. 5.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 28 (c) 56 (d) 49
  6. 6.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 729 (d) 756
  7. 7.What is the 12th term of the AP 5, 9, 13, 17, …? (a) 49 (b) 44 (c) 48 (d) 53
  8. 8.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 70 (b) 35 (c) 36 (d) 8
  9. 9.What is the sum of all the whole numbers from 1 to 20? (a) 420 (b) 200 (c) 190 (d) 210
  10. 10.What is the sum of all the whole numbers from 1 to 34? (a) 1190 (b) 595 (c) 561 (d) 578
  11. 11.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 354 (b) 708 (c) 57 (d) 384
  12. 12.Which term of the AP 1, 7, 13, 19, … is 103? (a) 20th (b) 18th (c) 19th (d) 17th
  13. 13.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 108 (b) 16 (c) 216 (d) 109
  14. 14.What is the 27th term of the AP 10, 16, 22, 28, …? (a) 172 (b) 156 (c) 166 (d) 162
  15. 15.What is the sum of all the whole numbers from 1 to 95? (a) 4560 (b) 4561 (c) 9120 (d) 4465
  16. 16.Which term of the AP 2, 6, 10, 14, … is 146? (a) 39th (b) 37th (c) 38th (d) 36th
  17. 17.What is the 32nd term of the AP 13, 17, 21, 25, …? (a) 137 (b) 141 (c) 128 (d) 124
  18. 18.What is the 40th term of the AP 7, 11, 15, 19, …? (a) 156 (b) 160 (c) 167 (d) 163
  19. 19.Which term of the AP 7, 12, 17, 22, … is 157? (a) 30th (b) 32nd (c) 31st (d) 33rd
  20. 20.What is the sum of all the whole numbers from 1 to 70? (a) 2450 (b) 2485 (c) 2415 (d) 4970
  21. 21.What is the sum of the first 7 terms of the AP 2, 8, 14, …? (a) 38 (b) 161 (c) 140 (d) 280
  22. 22.What is the 20th term of the AP 4, 10, 16, 22, …? (a) 114 (b) 120 (c) 124 (d) 118
  23. 23.Which term of the AP 4, 12, 20, 28, … is 276? (a) 37th (b) 36th (c) 35th (d) 34th
  24. 24.What is the sum of the first 7 terms of the AP 6, 10, 14, …? (a) 126 (b) 252 (c) 140 (d) 30
  25. 25.What is the sum of all the whole numbers from 1 to 25? (a) 300 (b) 650 (c) 326 (d) 325
  26. 26.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 135 (b) 27 (c) 138 (d) 270
  27. 27.What is the missing term in the AP 6, ?, 24, 33, 42? (a) 14 (b) 24 (c) 16 (d) 15
  28. 28.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 186 (b) 108 (c) 28 (d) 93
  29. 29.What is the sum of the first 10 terms of the AP 5, 7, 9, …? (a) 23 (b) 150 (c) 140 (d) 280
  30. 30.What is the sum of all the whole numbers from 1 to 39? (a) 741 (b) 780 (c) 1560 (d) 781
  31. 31.What is the 22nd term of the AP 11, 16, 21, 26, …? (a) 116 (b) 121 (c) 110 (d) 105
  32. 32.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 133 (b) 154 (c) 266 (d) 37
  33. 33.What is the 12th term of the AP 20, 24, 28, 32, …? (a) 64 (b) 68 (c) 48 (d) 44
  34. 34.Which term of the AP 15, 20, 25, 30, … is 50? (a) 10th (b) 8th (c) 7th (d) 9th
  35. 35.What is the 14th term of the AP 11, 17, 23, 29, …? (a) 89 (b) 95 (c) 78 (d) 84
  36. 36.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 756 (c) 379 (d) 378
  37. 37.What is the missing term in the AP 14, ?, 30, 38, 46? (a) 23 (b) 30 (c) 21 (d) 22
  38. 38.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 13 (b) 12 (c) 10 (d) 11
  39. 39.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 324 (c) 171 (d) 342
  40. 40.What is the sum of all the whole numbers from 1 to 80? (a) 3160 (b) 6480 (c) 3200 (d) 3240

Answer key

  1. 243
  2. 33rd
  3. 83
  4. 83
  5. 49
  6. 729
  7. 49
  8. 35
  9. 210
  10. 595
  11. 354
  12. 18th
  13. 108
  14. 166
  15. 4560
  16. 37th
  17. 137
  18. 163
  19. 31st
  20. 2485
  21. 140
  22. 118
  23. 35th
  24. 126
  25. 325
  26. 135
  27. 15
  28. 93
  29. 140
  30. 780
  31. 116
  32. 133
  33. 64
  34. 8th
  35. 89
  36. 378
  37. 22
  38. 11
  39. 324
  40. 3240

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