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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 464 · 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 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 650 (d) 625
  2. 2.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 320 (b) 160 (c) 25 (d) 170
  3. 3.What is the 34th term of the AP 12, 18, 24, 30, …? (a) 204 (b) 198 (c) 210 (d) 216
  4. 4.What is the missing term in the AP 7, 14, 21, ?, 35? (a) 27 (b) 28 (c) 35 (d) 29
  5. 5.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 104 (b) 10 (c) 56 (d) 52
  6. 6.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 15 (c) 64 (d) 36
  7. 7.What is the 39th term of the AP 8, 14, 20, 26, …? (a) 236 (b) 242 (c) 234 (d) 228
  8. 8.Which term of the AP 7, 16, 25, 34, … is 322? (a) 37th (b) 35th (c) 36th (d) 38th
  9. 9.What is the missing term in the AP 7, 13, ?, 25, 31? (a) 20 (b) 19 (c) 25 (d) 18
  10. 10.What is the missing term in the AP 9, ?, 27, 36, 45? (a) 17 (b) 27 (c) 18 (d) 19
  11. 11.Which term of the AP 16, 19, 22, 25, … is 112? (a) 32nd (b) 35th (c) 33rd (d) 34th
  12. 12.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 306 (c) 153 (d) 289
  13. 13.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 252 (b) 240 (c) 480 (d) 31
  14. 14.What is the missing term in the AP 20, 23, ?, 29, 32? (a) 27 (b) 25 (c) 29 (d) 26
  15. 15.What is the sum of all the whole numbers from 1 to 66? (a) 2211 (b) 2178 (c) 2145 (d) 4422
  16. 16.What is the 30th term of the AP 1, 6, 11, 16, …? (a) 151 (b) 146 (c) 150 (d) 145
  17. 17.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 108 (b) 33 (c) 126 (d) 216
  18. 18.What is the sum of all the whole numbers from 1 to 47? (a) 1128 (b) 2256 (c) 1081 (d) 1129
  19. 19.What is the missing term in the AP 10, 19, 28, ?, 46? (a) 38 (b) 36 (c) 46 (d) 37
  20. 20.What is the 23rd term of the AP 1, 10, 19, 28, …? (a) 208 (b) 198 (c) 199 (d) 207
  21. 21.What is the sum of the first 10 terms of the AP 9, 14, 19, …? (a) 54 (b) 340 (c) 630 (d) 315
  22. 22.What is the 15th term of the AP 3, 11, 19, 27, …? (a) 115 (b) 120 (c) 112 (d) 123
  23. 23.What is the 26th term of the AP 9, 18, 27, 36, …? (a) 243 (b) 225 (c) 235 (d) 234
  24. 24.Which term of the AP 15, 19, 23, 27, … is 51? (a) 11th (b) 9th (c) 12th (d) 10th
  25. 25.What is the sum of the first 6 terms of the AP 8, 11, 14, …? (a) 23 (b) 186 (c) 102 (d) 93
  26. 26.What is the 17th term of the AP 8, 12, 16, 20, …? (a) 72 (b) 76 (c) 68 (d) 64
  27. 27.What is the sum of the first 8 terms of the AP 6, 7, 8, …? (a) 152 (b) 13 (c) 76 (d) 80
  28. 28.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 990 (c) 1035 (d) 2070
  29. 29.What is the sum of all the whole numbers from 1 to 39? (a) 741 (b) 781 (c) 780 (d) 1560
  30. 30.What is the sum of the first 7 terms of the AP 4, 6, 8, …? (a) 140 (b) 70 (c) 77 (d) 16
  31. 31.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 136 (c) 272 (d) 256
  32. 32.What is the missing term in the AP 6, 11, ?, 21, 26? (a) 17 (b) 21 (c) 16 (d) 15
  33. 33.What is the 34th term of the AP 18, 26, 34, 42, …? (a) 272 (b) 282 (c) 290 (d) 264
  34. 34.What is the sum of all the whole numbers from 1 to 55? (a) 1541 (b) 1540 (c) 3080 (d) 1485
  35. 35.What is the sum of all the whole numbers from 1 to 29? (a) 435 (b) 436 (c) 406 (d) 870
  36. 36.What is the 15th term of the AP 12, 15, 18, 21, …? (a) 54 (b) 57 (c) 45 (d) 42
  37. 37.What is the missing term in the AP 14, ?, 28, 35, 42? (a) 28 (b) 22 (c) 20 (d) 21
  38. 38.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 702 (c) 351 (d) 676
  39. 39.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 270 (b) 140 (c) 18 (d) 135
  40. 40.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 22 (b) 94 (c) 182 (d) 91

Answer key

  1. 625
  2. 160
  3. 210
  4. 28
  5. 52
  6. 64
  7. 236
  8. 36th
  9. 19
  10. 18
  11. 33rd
  12. 289
  13. 240
  14. 26
  15. 2211
  16. 146
  17. 108
  18. 1128
  19. 37
  20. 199
  21. 315
  22. 115
  23. 234
  24. 10th
  25. 93
  26. 72
  27. 76
  28. 1035
  29. 780
  30. 70
  31. 256
  32. 16
  33. 282
  34. 1540
  35. 435
  36. 54
  37. 21
  38. 676
  39. 135
  40. 91

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