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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 452 · 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 7 terms of the AP 1, 2, 3, …? (a) 56 (b) 7 (c) 29 (d) 28
  2. 2.What is the sum of all the whole numbers from 1 to 47? (a) 2256 (b) 1081 (c) 1129 (d) 1128
  3. 3.What is the sum of the first 7 terms of the AP 4, 6, 8, …? (a) 70 (b) 140 (c) 77 (d) 16
  4. 4.Which term of the AP 1, 8, 15, 22, … is 134? (a) 19th (b) 21st (c) 20th (d) 22nd
  5. 5.What is the sum of the first 5 terms of the AP 3, 9, 15, …? (a) 75 (b) 150 (c) 90 (d) 27
  6. 6.What is the sum of the first 7 terms of the AP 9, 14, 19, …? (a) 168 (b) 173 (c) 39 (d) 336
  7. 7.What is the sum of all the whole numbers from 1 to 72? (a) 2628 (b) 5256 (c) 2592 (d) 2556
  8. 8.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 302 (b) 52 (c) 594 (d) 297
  9. 9.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 465 (c) 930 (d) 900
  10. 10.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 33 (c) 289 (d) 306
  11. 11.What is the missing term in the AP 4, ?, 16, 22, 28? (a) 11 (b) 9 (c) 16 (d) 10
  12. 12.What is the 31st term of the AP 16, 24, 32, 40, …? (a) 256 (b) 240 (c) 264 (d) 248
  13. 13.What is the missing term in the AP 15, 19, ?, 27, 31? (a) 24 (b) 22 (c) 27 (d) 23
  14. 14.What is the missing term in the AP 2, 8, 14, ?, 26? (a) 21 (b) 26 (c) 19 (d) 20
  15. 15.Which term of the AP 12, 20, 28, 36, … is 76? (a) 8th (b) 9th (c) 10th (d) 11th
  16. 16.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 110 (c) 50 (d) 55
  17. 17.What is the sum of the first 8 terms of the AP 9, 13, 17, …? (a) 37 (b) 184 (c) 200 (d) 368
  18. 18.What is the missing term in the AP 10, ?, 28, 37, 46? (a) 28 (b) 18 (c) 19 (d) 20
  19. 19.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 20 (b) 84 (c) 150 (d) 75
  20. 20.What is the 11th term of the AP 7, 10, 13, 16, …? (a) 37 (b) 33 (c) 40 (d) 30
  21. 21.What is the sum of the first 11 terms of the AP 9, 13, 17, …? (a) 319 (b) 49 (c) 638 (d) 341
  22. 22.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 156 (b) 23 (c) 90 (d) 78
  23. 23.Which term of the AP 4, 12, 20, 28, … is 124? (a) 15th (b) 18th (c) 17th (d) 16th
  24. 24.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 130 (b) 65 (c) 70 (d) 23
  25. 25.What is the sum of all the whole numbers from 1 to 50? (a) 1250 (b) 2550 (c) 1225 (d) 1275
  26. 26.What is the 11th term of the AP 4, 13, 22, 31, …? (a) 103 (b) 99 (c) 94 (d) 90
  27. 27.What is the 40th term of the AP 15, 21, 27, 33, …? (a) 249 (b) 255 (c) 240 (d) 234
  28. 28.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 63 (b) 56 (c) 112 (d) 14
  29. 29.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 210 (b) 24 (c) 105 (d) 108
  30. 30.What is the missing term in the AP 14, 17, ?, 23, 26? (a) 23 (b) 19 (c) 20 (d) 21
  31. 31.What is the sum of the first 10 terms of the AP 2, 5, 8, …? (a) 29 (b) 155 (c) 170 (d) 310
  32. 32.What is the sum of the first 6 terms of the AP 3, 6, 9, …? (a) 18 (b) 126 (c) 63 (d) 72
  33. 33.What is the sum of the first 12 terms of the AP 8, 9, 10, …? (a) 19 (b) 162 (c) 168 (d) 324
  34. 34.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 35 (b) 38 (c) 70 (d) 13
  35. 35.What is the missing term in the AP 19, 25, ?, 37, 43? (a) 37 (b) 31 (c) 32 (d) 30
  36. 36.What is the sum of all the whole numbers from 1 to 87? (a) 3828 (b) 7656 (c) 3829 (d) 3741
  37. 37.What is the 27th term of the AP 8, 16, 24, 32, …? (a) 224 (b) 208 (c) 216 (d) 217
  38. 38.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 50 (b) 18 (c) 60 (d) 100
  39. 39.What is the missing term in the AP 13, 17, 21, ?, 29? (a) 24 (b) 29 (c) 26 (d) 25
  40. 40.What is the sum of all the whole numbers from 1 to 53? (a) 1431 (b) 1378 (c) 1432 (d) 2862

Answer key

  1. 28
  2. 1128
  3. 70
  4. 20th
  5. 75
  6. 168
  7. 2628
  8. 297
  9. 900
  10. 289
  11. 10
  12. 256
  13. 23
  14. 20
  15. 9th
  16. 55
  17. 184
  18. 19
  19. 75
  20. 37
  21. 319
  22. 78
  23. 16th
  24. 65
  25. 1275
  26. 94
  27. 249
  28. 56
  29. 105
  30. 20
  31. 155
  32. 63
  33. 162
  34. 35
  35. 31
  36. 3828
  37. 216
  38. 50
  39. 25
  40. 1431

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