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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 146 · 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 6 terms of the AP 1, 4, 7, …? (a) 60 (b) 51 (c) 16 (d) 102
  2. 2.What is the 26th term of the AP 15, 19, 23, 27, …? (a) 115 (b) 119 (c) 104 (d) 100
  3. 3.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 552 (c) 276 (d) 45
  4. 4.What is the sum of the first 12 terms of the AP 6, 8, 10, …? (a) 28 (b) 408 (c) 204 (d) 216
  5. 5.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 35 (c) 324 (d) 342
  6. 6.What is the sum of all the whole numbers from 1 to 35? (a) 1260 (b) 630 (c) 595 (d) 631
  7. 7.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 47 (b) 300 (c) 324 (d) 600
  8. 8.What is the sum of all the whole numbers from 1 to 88? (a) 7832 (b) 3872 (c) 3828 (d) 3916
  9. 9.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 32 (b) 204 (c) 120 (d) 102
  10. 10.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 64 (c) 15 (d) 36
  11. 11.What is the 13th term of the AP 14, 17, 20, 23, …? (a) 36 (b) 50 (c) 53 (d) 39
  12. 12.Which term of the AP 7, 11, 15, 19, … is 119? (a) 29th (b) 31st (c) 30th (d) 28th
  13. 13.What is the sum of the first 12 terms of the AP 3, 4, 5, …? (a) 204 (b) 108 (c) 14 (d) 102
  14. 14.What is the 38th term of the AP 2, 7, 12, 17, …? (a) 185 (b) 190 (c) 187 (d) 192
  15. 15.What is the missing term in the AP 7, 16, 25, ?, 43? (a) 35 (b) 33 (c) 34 (d) 43
  16. 16.What is the sum of all the whole numbers from 1 to 80? (a) 3160 (b) 3240 (c) 6480 (d) 3200
  17. 17.What is the 23rd term of the AP 10, 15, 20, 25, …? (a) 120 (b) 115 (c) 110 (d) 125
  18. 18.What is the 19th term of the AP 10, 12, 14, 16, …? (a) 38 (b) 48 (c) 46 (d) 36
  19. 19.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 396 (b) 203 (c) 198 (d) 42
  20. 20.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 15 (b) 220 (c) 110 (d) 111
  21. 21.Which term of the AP 2, 11, 20, 29, … is 182? (a) 21st (b) 22nd (c) 20th (d) 23rd
  22. 22.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 378 (c) 756 (d) 379
  23. 23.What is the sum of all the whole numbers from 1 to 70? (a) 2415 (b) 4970 (c) 2450 (d) 2485
  24. 24.What is the sum of all the whole numbers from 1 to 33? (a) 528 (b) 562 (c) 1122 (d) 561
  25. 25.What is the 22nd term of the AP 4, 9, 14, 19, …? (a) 114 (b) 110 (c) 105 (d) 109
  26. 26.What is the sum of all the whole numbers from 1 to 50? (a) 1225 (b) 1275 (c) 1250 (d) 2550
  27. 27.What is the sum of all the whole numbers from 1 to 95? (a) 9120 (b) 4560 (c) 4561 (d) 4465
  28. 28.What is the 31st term of the AP 9, 13, 17, 21, …? (a) 120 (b) 133 (c) 124 (d) 129
  29. 29.What is the 11th term of the AP 1, 5, 9, 13, …? (a) 41 (b) 44 (c) 40 (d) 45
  30. 30.Which term of the AP 16, 21, 26, 31, … is 56? (a) 8th (b) 11th (c) 10th (d) 9th
  31. 31.What is the 30th term of the AP 18, 27, 36, 45, …? (a) 279 (b) 270 (c) 288 (d) 261
  32. 32.Which term of the AP 8, 16, 24, 32, … is 136? (a) 16th (b) 19th (c) 17th (d) 18th
  33. 33.What is the 18th term of the AP 10, 14, 18, 22, …? (a) 72 (b) 68 (c) 78 (d) 82
  34. 34.What is the 13th term of the AP 5, 8, 11, 14, …? (a) 44 (b) 39 (c) 36 (d) 41
  35. 35.What is the 17th term of the AP 17, 19, 21, 23, …? (a) 51 (b) 32 (c) 34 (d) 49
  36. 36.Which term of the AP 15, 18, 21, 24, … is 42? (a) 9th (b) 10th (c) 14th (d) 11th
  37. 37.What is the sum of the first 10 terms of the AP 4, 9, 14, …? (a) 49 (b) 290 (c) 530 (d) 265
  38. 38.Which term of the AP 16, 23, 30, 37, … is 142? (a) 21st (b) 20th (c) 18th (d) 19th
  39. 39.What is the missing term in the AP 11, ?, 21, 26, 31? (a) 21 (b) 17 (c) 16 (d) 15
  40. 40.Which term of the AP 15, 17, 19, 21, … is 45? (a) 18th (b) 16th (c) 17th (d) 15th

Answer key

  1. 51
  2. 115
  3. 529
  4. 204
  5. 324
  6. 630
  7. 300
  8. 3916
  9. 102
  10. 64
  11. 50
  12. 29th
  13. 102
  14. 187
  15. 34
  16. 3240
  17. 120
  18. 46
  19. 198
  20. 110
  21. 21st
  22. 378
  23. 2485
  24. 561
  25. 109
  26. 1275
  27. 4560
  28. 129
  29. 41
  30. 9th
  31. 279
  32. 17th
  33. 78
  34. 41
  35. 49
  36. 10th
  37. 265
  38. 19th
  39. 16
  40. 16th

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