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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 604 · 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 sum of the first 8 terms of the AP 5, 7, 9, …? (a) 104 (b) 96 (c) 19 (d) 192
  2. 2.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 858 (b) 69 (c) 429 (d) 462
  3. 3.What is the sum of all the whole numbers from 1 to 43? (a) 903 (b) 947 (c) 946 (d) 1892
  4. 4.What is the 26th term of the AP 6, 15, 24, 33, …? (a) 225 (b) 240 (c) 234 (d) 231
  5. 5.What is the 17th term of the AP 4, 11, 18, 25, …? (a) 119 (b) 123 (c) 116 (d) 112
  6. 6.What is the sum of the first 8 terms of the AP 10, 14, 18, …? (a) 192 (b) 208 (c) 38 (d) 384
  7. 7.What is the 11th term of the AP 10, 14, 18, 22, …? (a) 54 (b) 44 (c) 50 (d) 40
  8. 8.What is the 23rd term of the AP 11, 20, 29, 38, …? (a) 209 (b) 207 (c) 218 (d) 198
  9. 9.What is the sum of the first 10 terms of the AP 7, 11, 15, …? (a) 250 (b) 43 (c) 270 (d) 500
  10. 10.What is the sum of the first 7 terms of the AP 5, 11, 17, …? (a) 322 (b) 182 (c) 161 (d) 41
  11. 11.What is the sum of all the whole numbers from 1 to 26? (a) 325 (b) 702 (c) 338 (d) 351
  12. 12.What is the sum of the first 10 terms of the AP 10, 14, 18, …? (a) 280 (b) 300 (c) 46 (d) 560
  13. 13.What is the sum of all the whole numbers from 1 to 62? (a) 1953 (b) 3906 (c) 1922 (d) 1891
  14. 14.What is the sum of the first 10 terms of the AP 10, 11, 12, …? (a) 145 (b) 19 (c) 290 (d) 150
  15. 15.What is the sum of the first 11 terms of the AP 2, 5, 8, …? (a) 374 (b) 190 (c) 187 (d) 32
  16. 16.What is the sum of the first 7 terms of the AP 1, 5, 9, …? (a) 25 (b) 105 (c) 91 (d) 182
  17. 17.Which term of the AP 13, 16, 19, 22, … is 61? (a) 18th (b) 17th (c) 16th (d) 19th
  18. 18.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 17 (b) 216 (c) 112 (d) 108
  19. 19.What is the 36th term of the AP 13, 20, 27, 34, …? (a) 258 (b) 245 (c) 252 (d) 265
  20. 20.What is the 31st term of the AP 2, 7, 12, 17, …? (a) 157 (b) 152 (c) 155 (d) 150
  21. 21.Which term of the AP 4, 8, 12, 16, … is 56? (a) 13th (b) 16th (c) 15th (d) 14th
  22. 22.Which term of the AP 15, 18, 21, 24, … is 75? (a) 21st (b) 25th (c) 20th (d) 22nd
  23. 23.What is the 20th term of the AP 20, 29, 38, 47, …? (a) 171 (b) 191 (c) 180 (d) 200
  24. 24.Which term of the AP 11, 13, 15, 17, … is 63? (a) 26th (b) 27th (c) 28th (d) 29th
  25. 25.What is the 19th term of the AP 19, 22, 25, 28, …? (a) 73 (b) 57 (c) 76 (d) 54
  26. 26.What is the sum of all the whole numbers from 1 to 41? (a) 861 (b) 862 (c) 820 (d) 1722
  27. 27.What is the missing term in the AP 10, ?, 20, 25, 30? (a) 20 (b) 16 (c) 14 (d) 15
  28. 28.What is the sum of the first 10 terms of the AP 10, 15, 20, …? (a) 55 (b) 325 (c) 650 (d) 350
  29. 29.What is the sum of all the whole numbers from 1 to 57? (a) 1596 (b) 1654 (c) 1653 (d) 3306
  30. 30.What is the 31st term of the AP 2, 4, 6, 8, …? (a) 63 (b) 62 (c) 60 (d) 64
  31. 31.What is the missing term in the AP 16, ?, 32, 40, 48? (a) 23 (b) 32 (c) 24 (d) 25
  32. 32.What is the 21st term of the AP 3, 12, 21, 30, …? (a) 183 (b) 192 (c) 189 (d) 180
  33. 33.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 114 (b) 57 (c) 66 (d) 17
  34. 34.What is the sum of all the whole numbers from 1 to 71? (a) 2557 (b) 5112 (c) 2485 (d) 2556
  35. 35.What is the sum of all the whole numbers from 1 to 96? (a) 4656 (b) 4608 (c) 9312 (d) 4560
  36. 36.What is the missing term in the AP 14, ?, 32, 41, 50? (a) 24 (b) 23 (c) 32 (d) 22
  37. 37.What is the 23rd term of the AP 1, 9, 17, 25, …? (a) 184 (b) 177 (c) 185 (d) 176
  38. 38.Which term of the AP 9, 16, 23, 30, … is 93? (a) 13th (b) 14th (c) 15th (d) 12th
  39. 39.What is the 18th term of the AP 16, 21, 26, 31, …? (a) 106 (b) 90 (c) 85 (d) 101
  40. 40.What is the sum of all the whole numbers from 1 to 93? (a) 4372 (b) 4278 (c) 8742 (d) 4371

Answer key

  1. 96
  2. 429
  3. 946
  4. 231
  5. 116
  6. 192
  7. 50
  8. 209
  9. 250
  10. 161
  11. 351
  12. 280
  13. 1953
  14. 145
  15. 187
  16. 91
  17. 17th
  18. 108
  19. 258
  20. 152
  21. 14th
  22. 21st
  23. 191
  24. 27th
  25. 73
  26. 861
  27. 15
  28. 325
  29. 1653
  30. 62
  31. 24
  32. 183
  33. 57
  34. 2556
  35. 4656
  36. 23
  37. 177
  38. 13th
  39. 101
  40. 4371

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