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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 767 · 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 all the whole numbers from 1 to 54? (a) 1485 (b) 1458 (c) 2970 (d) 1431
  2. 2.What is the missing term in the AP 5, 12, 19, ?, 33? (a) 27 (b) 25 (c) 26 (d) 33
  3. 3.What is the 19th term of the AP 18, 26, 34, 42, …? (a) 152 (b) 144 (c) 170 (d) 162
  4. 4.What is the 10th term of the AP 20, 22, 24, 26, …? (a) 20 (b) 18 (c) 38 (d) 40
  5. 5.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 92 (c) 78 (d) 91
  6. 6.What is the 40th term of the AP 18, 20, 22, 24, …? (a) 80 (b) 78 (c) 96 (d) 98
  7. 7.What is the sum of all the whole numbers from 1 to 48? (a) 1128 (b) 1176 (c) 2352 (d) 1152
  8. 8.What is the sum of all the whole numbers from 1 to 36? (a) 1332 (b) 648 (c) 630 (d) 666
  9. 9.What is the missing term in the AP 14, 19, 24, ?, 34? (a) 34 (b) 30 (c) 29 (d) 28
  10. 10.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 19 (c) 55 (d) 100
  11. 11.What is the missing term in the AP 6, 11, ?, 21, 26? (a) 16 (b) 15 (c) 17 (d) 21
  12. 12.What is the 29th term of the AP 6, 10, 14, 18, …? (a) 116 (b) 118 (c) 122 (d) 112
  13. 13.What is the sum of all the whole numbers from 1 to 22? (a) 506 (b) 253 (c) 242 (d) 231
  14. 14.What is the missing term in the AP 13, ?, 31, 40, 49? (a) 22 (b) 31 (c) 23 (d) 21
  15. 15.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 160 (b) 170 (c) 320 (d) 25
  16. 16.What is the missing term in the AP 16, 20, ?, 28, 32? (a) 25 (b) 24 (c) 28 (d) 23
  17. 17.What is the 10th term of the AP 10, 13, 16, 19, …? (a) 30 (b) 37 (c) 40 (d) 27
  18. 18.What is the sum of all the whole numbers from 1 to 11? (a) 132 (b) 67 (c) 55 (d) 66
  19. 19.What is the missing term in the AP 12, 14, 16, ?, 20? (a) 19 (b) 18 (c) 17 (d) 20
  20. 20.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 42 (c) 36 (d) 21
  21. 21.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 15 (c) 36 (d) 64
  22. 22.Which term of the AP 1, 8, 15, 22, … is 190? (a) 28th (b) 29th (c) 27th (d) 30th
  23. 23.What is the sum of the first 11 terms of the AP 4, 6, 8, …? (a) 24 (b) 308 (c) 165 (d) 154
  24. 24.What is the 40th term of the AP 5, 7, 9, 11, …? (a) 85 (b) 78 (c) 80 (d) 83
  25. 25.What is the 38th term of the AP 19, 23, 27, 31, …? (a) 152 (b) 148 (c) 167 (d) 171
  26. 26.What is the 12th term of the AP 3, 5, 7, 9, …? (a) 27 (b) 22 (c) 25 (d) 24
  27. 27.What is the 24th term of the AP 15, 22, 29, 36, …? (a) 161 (b) 183 (c) 168 (d) 176
  28. 28.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 35 (b) 336 (c) 168 (d) 184
  29. 29.What is the missing term in the AP 11, ?, 19, 23, 27? (a) 19 (b) 16 (c) 14 (d) 15
  30. 30.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 120 (b) 63 (c) 18 (d) 60
  31. 31.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 480 (b) 960 (c) 516 (d) 73
  32. 32.What is the sum of all the whole numbers from 1 to 83? (a) 3487 (b) 3403 (c) 3486 (d) 6972
  33. 33.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 81 (c) 45 (d) 90
  34. 34.What is the sum of all the whole numbers from 1 to 46? (a) 1058 (b) 2162 (c) 1035 (d) 1081
  35. 35.What is the missing term in the AP 7, 14, 21, ?, 35? (a) 35 (b) 29 (c) 27 (d) 28
  36. 36.What is the sum of all the whole numbers from 1 to 50? (a) 1225 (b) 1250 (c) 1275 (d) 2550
  37. 37.What is the 26th term of the AP 9, 15, 21, 27, …? (a) 156 (b) 165 (c) 159 (d) 150
  38. 38.What is the sum of the first 11 terms of the AP 8, 13, 18, …? (a) 58 (b) 726 (c) 368 (d) 363
  39. 39.What is the 26th term of the AP 1, 5, 9, 13, …? (a) 100 (b) 104 (c) 101 (d) 105
  40. 40.What is the sum of all the whole numbers from 1 to 67? (a) 2278 (b) 4556 (c) 2279 (d) 2211

Answer key

  1. 1485
  2. 26
  3. 162
  4. 38
  5. 91
  6. 96
  7. 1176
  8. 666
  9. 29
  10. 100
  11. 16
  12. 118
  13. 253
  14. 22
  15. 160
  16. 24
  17. 37
  18. 66
  19. 18
  20. 36
  21. 64
  22. 28th
  23. 154
  24. 83
  25. 167
  26. 25
  27. 176
  28. 168
  29. 15
  30. 60
  31. 480
  32. 3486
  33. 81
  34. 1081
  35. 28
  36. 1275
  37. 159
  38. 363
  39. 101
  40. 2278

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