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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 846 · 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 33rd term of the AP 8, 14, 20, 26, …? (a) 200 (b) 198 (c) 206 (d) 192
  2. 2.What is the missing term in the AP 16, ?, 22, 25, 28? (a) 22 (b) 18 (c) 19 (d) 20
  3. 3.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 72 (d) 64
  4. 4.What is the 20th term of the AP 9, 13, 17, 21, …? (a) 85 (b) 80 (c) 76 (d) 89
  5. 5.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 91 (c) 25 (d) 182
  6. 6.What is the missing term in the AP 1, 3, ?, 7, 9? (a) 7 (b) 6 (c) 4 (d) 5
  7. 7.What is the 18th term of the AP 10, 13, 16, 19, …? (a) 64 (b) 54 (c) 61 (d) 51
  8. 8.What is the sum of all the whole numbers from 1 to 33? (a) 1122 (b) 562 (c) 561 (d) 528
  9. 9.What is the missing term in the AP 11, 19, ?, 35, 43? (a) 35 (b) 26 (c) 28 (d) 27
  10. 10.What is the missing term in the AP 8, 17, ?, 35, 44? (a) 25 (b) 26 (c) 35 (d) 27
  11. 11.What is the 16th term of the AP 7, 15, 23, 31, …? (a) 120 (b) 127 (c) 128 (d) 135
  12. 12.What is the sum of all the whole numbers from 1 to 20? (a) 200 (b) 210 (c) 420 (d) 190
  13. 13.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 702 (c) 51 (d) 676
  14. 14.What is the 17th term of the AP 17, 22, 27, 32, …? (a) 85 (b) 102 (c) 80 (d) 97
  15. 15.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 704 (b) 62 (c) 385 (d) 352
  16. 16.What is the missing term in the AP 9, ?, 21, 27, 33? (a) 15 (b) 14 (c) 16 (d) 21
  17. 17.What is the sum of the first 5 terms of the AP 8, 14, 20, …? (a) 200 (b) 115 (c) 32 (d) 100
  18. 18.What is the missing term in the AP 14, ?, 30, 38, 46? (a) 22 (b) 23 (c) 30 (d) 21
  19. 19.What is the 21st term of the AP 6, 8, 10, 12, …? (a) 40 (b) 46 (c) 42 (d) 48
  20. 20.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 625 (c) 49 (d) 325
  21. 21.Which term of the AP 1, 9, 17, 25, … is 193? (a) 24th (b) 27th (c) 26th (d) 25th
  22. 22.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 19 (c) 100 (d) 110
  23. 23.What is the sum of the first 9 terms of the AP 7, 12, 17, …? (a) 243 (b) 248 (c) 486 (d) 47
  24. 24.What is the 28th term of the AP 5, 14, 23, 32, …? (a) 243 (b) 257 (c) 252 (d) 248
  25. 25.What is the 29th term of the AP 20, 23, 26, 29, …? (a) 84 (b) 87 (c) 107 (d) 104
  26. 26.Which term of the AP 1, 10, 19, 28, … is 298? (a) 33rd (b) 34th (c) 36th (d) 35th
  27. 27.What is the 10th term of the AP 6, 13, 20, 27, …? (a) 76 (b) 63 (c) 70 (d) 69
  28. 28.Which term of the AP 11, 20, 29, 38, … is 317? (a) 34th (b) 36th (c) 37th (d) 35th
  29. 29.Which term of the AP 10, 18, 26, 34, … is 226? (a) 30th (b) 28th (c) 29th (d) 27th
  30. 30.What is the 29th term of the AP 13, 22, 31, 40, …? (a) 261 (b) 252 (c) 265 (d) 274
  31. 31.What is the 13th term of the AP 13, 20, 27, 34, …? (a) 97 (b) 84 (c) 91 (d) 104
  32. 32.What is the sum of the first 9 terms of the AP 10, 15, 20, …? (a) 50 (b) 540 (c) 270 (d) 275
  33. 33.What is the 22nd term of the AP 16, 24, 32, 40, …? (a) 184 (b) 168 (c) 192 (d) 176
  34. 34.What is the sum of all the whole numbers from 1 to 63? (a) 2017 (b) 4032 (c) 2016 (d) 1953
  35. 35.What is the 30th term of the AP 18, 27, 36, 45, …? (a) 270 (b) 279 (c) 288 (d) 261
  36. 36.What is the sum of all the whole numbers from 1 to 39? (a) 780 (b) 781 (c) 1560 (d) 741
  37. 37.What is the 21st term of the AP 9, 17, 25, 33, …? (a) 168 (b) 177 (c) 160 (d) 169
  38. 38.What is the sum of the first 9 terms of the AP 6, 12, 18, …? (a) 297 (b) 270 (c) 540 (d) 54
  39. 39.What is the missing term in the AP 10, 19, 28, ?, 46? (a) 37 (b) 36 (c) 38 (d) 46
  40. 40.Which term of the AP 8, 16, 24, 32, … is 88? (a) 12th (b) 10th (c) 11th (d) 13th

Answer key

  1. 200
  2. 19
  3. 64
  4. 85
  5. 169
  6. 5
  7. 61
  8. 561
  9. 27
  10. 26
  11. 127
  12. 210
  13. 676
  14. 97
  15. 352
  16. 15
  17. 100
  18. 22
  19. 46
  20. 625
  21. 25th
  22. 100
  23. 243
  24. 248
  25. 104
  26. 34th
  27. 69
  28. 35th
  29. 28th
  30. 265
  31. 97
  32. 270
  33. 184
  34. 2016
  35. 279
  36. 780
  37. 169
  38. 270
  39. 37
  40. 11th

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