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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 214 · 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 37th term of the AP 2, 10, 18, 26, …? (a) 290 (b) 298 (c) 296 (d) 288
  2. 2.What is the sum of all the whole numbers from 1 to 83? (a) 6972 (b) 3487 (c) 3486 (d) 3403
  3. 3.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 25 (c) 91 (d) 169
  4. 4.What is the 35th term of the AP 16, 23, 30, 37, …? (a) 238 (b) 245 (c) 254 (d) 261
  5. 5.What is the sum of all the whole numbers from 1 to 35? (a) 630 (b) 1260 (c) 631 (d) 595
  6. 6.What is the sum of the first 6 terms of the AP 10, 15, 20, …? (a) 135 (b) 35 (c) 270 (d) 150
  7. 7.What is the missing term in the AP 6, ?, 24, 33, 42? (a) 16 (b) 24 (c) 15 (d) 14
  8. 8.What is the sum of all the whole numbers from 1 to 90? (a) 4050 (b) 8190 (c) 4095 (d) 4005
  9. 9.What is the missing term in the AP 17, 19, 21, ?, 25? (a) 25 (b) 22 (c) 23 (d) 24
  10. 10.What is the 21st term of the AP 15, 24, 33, 42, …? (a) 204 (b) 180 (c) 195 (d) 189
  11. 11.What is the missing term in the AP 9, ?, 17, 21, 25? (a) 12 (b) 17 (c) 14 (d) 13
  12. 12.What is the missing term in the AP 20, ?, 30, 35, 40? (a) 26 (b) 30 (c) 25 (d) 24
  13. 13.Which term of the AP 5, 7, 9, 11, … is 65? (a) 32nd (b) 31st (c) 30th (d) 33rd
  14. 14.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 60 (b) 35 (c) 10 (d) 30
  15. 15.Which term of the AP 15, 23, 31, 39, … is 303? (a) 36th (b) 38th (c) 39th (d) 37th
  16. 16.Which term of the AP 11, 15, 19, 23, … is 51? (a) 12th (b) 13th (c) 11th (d) 10th
  17. 17.What is the missing term in the AP 8, ?, 24, 32, 40? (a) 24 (b) 15 (c) 16 (d) 17
  18. 18.What is the 17th term of the AP 5, 11, 17, 23, …? (a) 101 (b) 102 (c) 107 (d) 96
  19. 19.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 90 (c) 45 (d) 81
  20. 20.What is the missing term in the AP 1, ?, 11, 16, 21? (a) 6 (b) 7 (c) 11 (d) 5
  21. 21.Which term of the AP 1, 5, 9, 13, … is 157? (a) 42nd (b) 41st (c) 40th (d) 39th
  22. 22.What is the 16th term of the AP 18, 20, 22, 24, …? (a) 50 (b) 30 (c) 48 (d) 32
  23. 23.Which term of the AP 14, 18, 22, 26, … is 110? (a) 24th (b) 27th (c) 26th (d) 25th
  24. 24.What is the sum of all the whole numbers from 1 to 10? (a) 50 (b) 55 (c) 45 (d) 110
  25. 25.What is the 40th term of the AP 10, 18, 26, 34, …? (a) 320 (b) 330 (c) 322 (d) 312
  26. 26.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 47 (c) 576 (d) 300
  27. 27.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 440 (b) 30 (c) 220 (d) 231
  28. 28.What is the sum of all the whole numbers from 1 to 80? (a) 3200 (b) 6480 (c) 3240 (d) 3160
  29. 29.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 95 (b) 31 (c) 190 (d) 110
  30. 30.What is the 14th term of the AP 18, 23, 28, 33, …? (a) 70 (b) 83 (c) 65 (d) 88
  31. 31.What is the 24th term of the AP 4, 10, 16, 22, …? (a) 144 (b) 148 (c) 138 (d) 142
  32. 32.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 812 (c) 784 (d) 55
  33. 33.What is the sum of the first 8 terms of the AP 10, 15, 20, …? (a) 220 (b) 45 (c) 440 (d) 240
  34. 34.What is the 15th term of the AP 8, 12, 16, 20, …? (a) 64 (b) 56 (c) 60 (d) 68
  35. 35.Which term of the AP 9, 12, 15, 18, … is 75? (a) 23rd (b) 22nd (c) 25th (d) 24th
  36. 36.What is the 34th term of the AP 3, 5, 7, 9, …? (a) 69 (b) 66 (c) 68 (d) 71
  37. 37.What is the 10th term of the AP 12, 17, 22, 27, …? (a) 57 (b) 50 (c) 62 (d) 45
  38. 38.What is the 24th term of the AP 2, 11, 20, 29, …? (a) 218 (b) 209 (c) 207 (d) 216
  39. 39.What is the sum of the first 10 terms of the AP 7, 12, 17, …? (a) 320 (b) 590 (c) 52 (d) 295
  40. 40.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 38 (b) 322 (c) 161 (d) 166

Answer key

  1. 290
  2. 3486
  3. 169
  4. 254
  5. 630
  6. 135
  7. 15
  8. 4095
  9. 23
  10. 195
  11. 13
  12. 25
  13. 31st
  14. 30
  15. 37th
  16. 11th
  17. 16
  18. 101
  19. 81
  20. 6
  21. 40th
  22. 48
  23. 25th
  24. 55
  25. 322
  26. 576
  27. 220
  28. 3240
  29. 95
  30. 83
  31. 142
  32. 784
  33. 220
  34. 64
  35. 23rd
  36. 69
  37. 57
  38. 209
  39. 295
  40. 161

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