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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 318 · 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 5 terms of the AP 9, 14, 19, …? (a) 100 (b) 29 (c) 190 (d) 95
  2. 2.What is the 13th term of the AP 17, 21, 25, 29, …? (a) 48 (b) 52 (c) 65 (d) 69
  3. 3.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 25 (b) 50 (c) 26 (d) 7
  4. 4.What is the missing term in the AP 19, 24, 29, ?, 39? (a) 39 (b) 33 (c) 34 (d) 35
  5. 5.What is the missing term in the AP 16, ?, 32, 40, 48? (a) 25 (b) 32 (c) 24 (d) 23
  6. 6.What is the 34th term of the AP 1, 8, 15, 22, …? (a) 238 (b) 239 (c) 232 (d) 231
  7. 7.What is the 27th term of the AP 11, 14, 17, 20, …? (a) 81 (b) 89 (c) 78 (d) 92
  8. 8.What is the missing term in the AP 4, 11, 18, ?, 32? (a) 24 (b) 25 (c) 26 (d) 32
  9. 9.Which term of the AP 6, 13, 20, 27, … is 153? (a) 22nd (b) 23rd (c) 21st (d) 24th
  10. 10.What is the missing term in the AP 5, 10, ?, 20, 25? (a) 14 (b) 15 (c) 20 (d) 16
  11. 11.What is the sum of all the whole numbers from 1 to 79? (a) 3081 (b) 6320 (c) 3161 (d) 3160
  12. 12.What is the sum of all the whole numbers from 1 to 55? (a) 1541 (b) 3080 (c) 1485 (d) 1540
  13. 13.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 756 (c) 379 (d) 378
  14. 14.What is the 32nd term of the AP 6, 11, 16, 21, …? (a) 166 (b) 160 (c) 161 (d) 155
  15. 15.What is the 13th term of the AP 20, 23, 26, 29, …? (a) 59 (b) 56 (c) 39 (d) 36
  16. 16.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 32 (b) 264 (c) 252 (d) 504
  17. 17.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 170 (b) 100 (c) 85 (d) 29
  18. 18.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 45 (c) 552 (d) 529
  19. 19.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 9 (c) 25 (d) 15
  20. 20.What is the 12th term of the AP 3, 9, 15, 21, …? (a) 72 (b) 69 (c) 66 (d) 75
  21. 21.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 378 (c) 756 (d) 53
  22. 22.What is the sum of all the whole numbers from 1 to 100? (a) 10100 (b) 5000 (c) 4950 (d) 5050
  23. 23.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 132 (c) 21 (d) 66
  24. 24.What is the sum of the first 6 terms of the AP 5, 9, 13, …? (a) 90 (b) 25 (c) 102 (d) 180
  25. 25.What is the sum of all the whole numbers from 1 to 67? (a) 2211 (b) 2279 (c) 4556 (d) 2278
  26. 26.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 342 (c) 35 (d) 324
  27. 27.What is the sum of the first 10 terms of the AP 6, 7, 8, …? (a) 210 (b) 110 (c) 15 (d) 105
  28. 28.What is the missing term in the AP 12, 19, ?, 33, 40? (a) 25 (b) 26 (c) 33 (d) 27
  29. 29.What is the 18th term of the AP 12, 21, 30, 39, …? (a) 162 (b) 174 (c) 165 (d) 153
  30. 30.What is the 29th term of the AP 16, 20, 24, 28, …? (a) 128 (b) 132 (c) 112 (d) 116
  31. 31.What is the 36th term of the AP 4, 10, 16, 22, …? (a) 216 (b) 220 (c) 210 (d) 214
  32. 32.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 78 (c) 156 (d) 66
  33. 33.What is the 28th term of the AP 20, 29, 38, 47, …? (a) 252 (b) 263 (c) 272 (d) 243
  34. 34.What is the sum of the first 8 terms of the AP 6, 7, 8, …? (a) 13 (b) 152 (c) 76 (d) 80
  35. 35.What is the sum of all the whole numbers from 1 to 43? (a) 903 (b) 946 (c) 1892 (d) 947
  36. 36.What is the 12th term of the AP 12, 19, 26, 33, …? (a) 84 (b) 96 (c) 89 (d) 77
  37. 37.What is the missing term in the AP 18, ?, 26, 30, 34? (a) 23 (b) 22 (c) 21 (d) 26
  38. 38.What is the sum of all the whole numbers from 1 to 68? (a) 2312 (b) 4692 (c) 2346 (d) 2278
  39. 39.What is the sum of all the whole numbers from 1 to 44? (a) 1980 (b) 990 (c) 968 (d) 946
  40. 40.What is the sum of the first 6 terms of the AP 9, 14, 19, …? (a) 129 (b) 144 (c) 258 (d) 34

Answer key

  1. 95
  2. 65
  3. 25
  4. 34
  5. 24
  6. 232
  7. 89
  8. 25
  9. 22nd
  10. 15
  11. 3160
  12. 1540
  13. 378
  14. 161
  15. 56
  16. 252
  17. 85
  18. 529
  19. 25
  20. 69
  21. 729
  22. 5050
  23. 121
  24. 90
  25. 2278
  26. 324
  27. 105
  28. 26
  29. 165
  30. 128
  31. 214
  32. 78
  33. 263
  34. 76
  35. 946
  36. 89
  37. 22
  38. 2346
  39. 990
  40. 129

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