← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 885 · 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 17th term of the AP 13, 21, 29, 37, …? (a) 136 (b) 128 (c) 141 (d) 149
  2. 2.What is the sum of all the whole numbers from 1 to 80? (a) 3200 (b) 3160 (c) 3240 (d) 6480
  3. 3.What is the 15th term of the AP 4, 13, 22, 31, …? (a) 130 (b) 139 (c) 126 (d) 135
  4. 4.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 84 (b) 90 (c) 19 (d) 168
  5. 5.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 42 (b) 396 (c) 203 (d) 198
  6. 6.Which term of the AP 17, 21, 25, 29, … is 65? (a) 12th (b) 14th (c) 13th (d) 15th
  7. 7.Which term of the AP 1, 3, 5, 7, … is 79? (a) 42nd (b) 40th (c) 39th (d) 41st
  8. 8.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 184 (b) 168 (c) 35 (d) 336
  9. 9.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 30 (d) 25
  10. 10.What is the sum of the first 12 terms of the AP 4, 7, 10, …? (a) 246 (b) 37 (c) 492 (d) 264
  11. 11.What is the sum of all the whole numbers from 1 to 70? (a) 2485 (b) 2450 (c) 4970 (d) 2415
  12. 12.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 812 (c) 55 (d) 406
  13. 13.What is the sum of all the whole numbers from 1 to 96? (a) 4560 (b) 9312 (c) 4656 (d) 4608
  14. 14.What is the missing term in the AP 6, ?, 14, 18, 22? (a) 9 (b) 14 (c) 11 (d) 10
  15. 15.What is the 18th term of the AP 2, 10, 18, 26, …? (a) 146 (b) 138 (c) 136 (d) 144
  16. 16.What is the sum of all the whole numbers from 1 to 30? (a) 465 (b) 435 (c) 450 (d) 930
  17. 17.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 91 (c) 169 (d) 182
  18. 18.What is the 15th term of the AP 19, 24, 29, 34, …? (a) 94 (b) 70 (c) 89 (d) 75
  19. 19.What is the sum of all the whole numbers from 1 to 47? (a) 1081 (b) 1128 (c) 2256 (d) 1129
  20. 20.What is the missing term in the AP 5, 12, 19, ?, 33? (a) 27 (b) 26 (c) 33 (d) 25
  21. 21.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 37 (c) 380 (d) 361
  22. 22.What is the 11th term of the AP 13, 20, 27, 34, …? (a) 90 (b) 83 (c) 77 (d) 70
  23. 23.What is the sum of all the whole numbers from 1 to 52? (a) 1378 (b) 1352 (c) 1326 (d) 2756
  24. 24.What is the sum of the first 11 terms of the AP 1, 4, 7, …? (a) 179 (b) 352 (c) 31 (d) 176
  25. 25.What is the missing term in the AP 1, 3, ?, 7, 9? (a) 5 (b) 6 (c) 7 (d) 4
  26. 26.What is the sum of the first 7 terms of the AP 5, 9, 13, …? (a) 119 (b) 29 (c) 238 (d) 133
  27. 27.What is the sum of all the whole numbers from 1 to 39? (a) 780 (b) 1560 (c) 781 (d) 741
  28. 28.What is the missing term in the AP 9, 14, ?, 24, 29? (a) 24 (b) 20 (c) 19 (d) 18
  29. 29.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 256 (b) 30 (c) 128 (d) 144
  30. 30.What is the sum of all the whole numbers from 1 to 64? (a) 2080 (b) 2048 (c) 2016 (d) 4160
  31. 31.What is the 26th term of the AP 13, 20, 27, 34, …? (a) 195 (b) 175 (c) 182 (d) 188
  32. 32.What is the 15th term of the AP 5, 7, 9, 11, …? (a) 30 (b) 28 (c) 35 (d) 33
  33. 33.Which term of the AP 17, 26, 35, 44, … is 359? (a) 41st (b) 38th (c) 40th (d) 39th
  34. 34.What is the sum of the first 12 terms of the AP 3, 4, 5, …? (a) 102 (b) 14 (c) 108 (d) 204
  35. 35.What is the missing term in the AP 3, 5, 7, ?, 11? (a) 11 (b) 8 (c) 9 (d) 10
  36. 36.What is the missing term in the AP 12, 14, ?, 18, 20? (a) 17 (b) 15 (c) 16 (d) 18
  37. 37.What is the sum of the first 7 terms of the AP 4, 5, 6, …? (a) 49 (b) 10 (c) 98 (d) 50
  38. 38.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 240 (c) 121 (d) 120
  39. 39.What is the 33rd term of the AP 6, 12, 18, 24, …? (a) 199 (b) 198 (c) 204 (d) 192
  40. 40.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 435 (c) 406 (d) 436

Answer key

  1. 141
  2. 3240
  3. 130
  4. 84
  5. 198
  6. 13th
  7. 40th
  8. 168
  9. 25
  10. 246
  11. 2485
  12. 784
  13. 4656
  14. 10
  15. 138
  16. 465
  17. 169
  18. 89
  19. 1128
  20. 26
  21. 361
  22. 83
  23. 1378
  24. 176
  25. 5
  26. 119
  27. 780
  28. 19
  29. 128
  30. 2080
  31. 188
  32. 33
  33. 39th
  34. 102
  35. 9
  36. 16
  37. 49
  38. 120
  39. 198
  40. 435

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