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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 514 · 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.Which term of the AP 3, 5, 7, 9, … is 27? (a) 12th (b) 15th (c) 14th (d) 13th
  2. 2.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 440 (b) 231 (c) 30 (d) 220
  3. 3.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 372 (b) 342 (c) 56 (d) 684
  4. 4.What is the 15th term of the AP 17, 19, 21, 23, …? (a) 30 (b) 47 (c) 45 (d) 28
  5. 5.What is the 11th term of the AP 17, 25, 33, 41, …? (a) 80 (b) 88 (c) 97 (d) 105
  6. 6.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 49 (c) 625 (d) 325
  7. 7.What is the sum of all the whole numbers from 1 to 79? (a) 3161 (b) 6320 (c) 3160 (d) 3081
  8. 8.What is the 35th term of the AP 18, 24, 30, 36, …? (a) 222 (b) 204 (c) 228 (d) 210
  9. 9.What is the 14th term of the AP 3, 5, 7, 9, …? (a) 26 (b) 28 (c) 29 (d) 31
  10. 10.What is the 14th term of the AP 12, 16, 20, 24, …? (a) 56 (b) 64 (c) 68 (d) 52
  11. 11.What is the sum of all the whole numbers from 1 to 28? (a) 812 (b) 392 (c) 378 (d) 406
  12. 12.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 64 (c) 15 (d) 72
  13. 13.What is the sum of all the whole numbers from 1 to 98? (a) 4753 (b) 4851 (c) 9702 (d) 4802
  14. 14.What is the sum of all the whole numbers from 1 to 62? (a) 1922 (b) 1891 (c) 1953 (d) 3906
  15. 15.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 600 (c) 576 (d) 47
  16. 16.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 70 (b) 40 (c) 11 (d) 35
  17. 17.What is the 27th term of the AP 12, 19, 26, 33, …? (a) 189 (b) 194 (c) 182 (d) 201
  18. 18.What is the 27th term of the AP 3, 7, 11, 15, …? (a) 108 (b) 111 (c) 104 (d) 107
  19. 19.What is the 29th term of the AP 1, 6, 11, 16, …? (a) 141 (b) 145 (c) 140 (d) 146
  20. 20.What is the 40th term of the AP 16, 24, 32, 40, …? (a) 328 (b) 320 (c) 312 (d) 336
  21. 21.Which term of the AP 20, 29, 38, 47, … is 191? (a) 20th (b) 19th (c) 21st (d) 22nd
  22. 22.What is the sum of the first 5 terms of the AP 1, 6, 11, …? (a) 21 (b) 60 (c) 55 (d) 110
  23. 23.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 385 (b) 62 (c) 704 (d) 352
  24. 24.What is the missing term in the AP 1, 4, 7, ?, 13? (a) 11 (b) 13 (c) 9 (d) 10
  25. 25.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 726 (b) 63 (c) 363 (d) 396
  26. 26.Which term of the AP 17, 21, 25, 29, … is 153? (a) 35th (b) 34th (c) 36th (d) 37th
  27. 27.Which term of the AP 4, 7, 10, 13, … is 88? (a) 28th (b) 29th (c) 31st (d) 30th
  28. 28.What is the sum of all the whole numbers from 1 to 71? (a) 5112 (b) 2485 (c) 2557 (d) 2556
  29. 29.What is the 37th term of the AP 11, 20, 29, 38, …? (a) 333 (b) 324 (c) 335 (d) 344
  30. 30.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 161 (b) 38 (c) 322 (d) 166
  31. 31.What is the 27th term of the AP 12, 15, 18, 21, …? (a) 78 (b) 81 (c) 93 (d) 90
  32. 32.What is the missing term in the AP 16, ?, 26, 31, 36? (a) 22 (b) 20 (c) 26 (d) 21
  33. 33.What is the sum of the first 7 terms of the AP 3, 6, 9, …? (a) 87 (b) 21 (c) 168 (d) 84
  34. 34.Which term of the AP 1, 6, 11, 16, … is 156? (a) 32nd (b) 31st (c) 34th (d) 33rd
  35. 35.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 150 (b) 75 (c) 80 (d) 12
  36. 36.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 497 (c) 496 (d) 465
  37. 37.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 342 (c) 324 (d) 35
  38. 38.What is the 27th term of the AP 19, 21, 23, 25, …? (a) 54 (b) 73 (c) 52 (d) 71
  39. 39.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 350 (b) 700 (c) 62 (d) 380
  40. 40.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 324 (b) 47 (c) 600 (d) 300

Answer key

  1. 13th
  2. 220
  3. 342
  4. 45
  5. 97
  6. 625
  7. 3160
  8. 222
  9. 29
  10. 64
  11. 406
  12. 64
  13. 4851
  14. 1953
  15. 576
  16. 35
  17. 194
  18. 107
  19. 141
  20. 328
  21. 20th
  22. 55
  23. 352
  24. 10
  25. 363
  26. 35th
  27. 29th
  28. 2556
  29. 335
  30. 161
  31. 90
  32. 21
  33. 84
  34. 32nd
  35. 75
  36. 496
  37. 324
  38. 71
  39. 350
  40. 300

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