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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 862 · 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 22nd term of the AP 11, 20, 29, 38, …? (a) 198 (b) 209 (c) 200 (d) 189
  2. 2.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 166 (b) 330 (c) 20 (d) 165
  3. 3.What is the 23rd term of the AP 20, 23, 26, 29, …? (a) 69 (b) 86 (c) 89 (d) 66
  4. 4.What is the sum of the first 11 terms of the AP 4, 7, 10, …? (a) 209 (b) 212 (c) 418 (d) 34
  5. 5.What is the 27th term of the AP 5, 11, 17, 23, …? (a) 167 (b) 156 (c) 161 (d) 162
  6. 6.What is the 22nd term of the AP 10, 19, 28, 37, …? (a) 189 (b) 198 (c) 208 (d) 199
  7. 7.What is the 16th term of the AP 1, 7, 13, 19, …? (a) 91 (b) 96 (c) 90 (d) 97
  8. 8.What is the sum of all the whole numbers from 1 to 49? (a) 1176 (b) 1226 (c) 2450 (d) 1225
  9. 9.What is the missing term in the AP 1, ?, 19, 28, 37? (a) 10 (b) 11 (c) 19 (d) 9
  10. 10.What is the 38th term of the AP 5, 10, 15, 20, …? (a) 191 (b) 190 (c) 185 (d) 195
  11. 11.What is the 22nd term of the AP 2, 7, 12, 17, …? (a) 110 (b) 107 (c) 105 (d) 112
  12. 12.What is the 35th term of the AP 15, 19, 23, 27, …? (a) 151 (b) 136 (c) 155 (d) 140
  13. 13.What is the sum of all the whole numbers from 1 to 42? (a) 861 (b) 882 (c) 1806 (d) 903
  14. 14.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 21 (c) 66 (d) 121
  15. 15.What is the sum of all the whole numbers from 1 to 64? (a) 2080 (b) 2016 (c) 2048 (d) 4160
  16. 16.What is the 22nd term of the AP 4, 10, 16, 22, …? (a) 136 (b) 130 (c) 132 (d) 126
  17. 17.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 144 (c) 78 (d) 23
  18. 18.What is the sum of all the whole numbers from 1 to 32? (a) 1056 (b) 512 (c) 496 (d) 528
  19. 19.Which term of the AP 9, 16, 23, 30, … is 219? (a) 33rd (b) 32nd (c) 31st (d) 30th
  20. 20.What is the sum of all the whole numbers from 1 to 99? (a) 4951 (b) 9900 (c) 4851 (d) 4950
  21. 21.What is the sum of all the whole numbers from 1 to 36? (a) 648 (b) 1332 (c) 630 (d) 666
  22. 22.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 350 (b) 31 (c) 190 (d) 175
  23. 23.What is the 16th term of the AP 17, 22, 27, 32, …? (a) 80 (b) 97 (c) 75 (d) 92
  24. 24.What is the sum of all the whole numbers from 1 to 82? (a) 3403 (b) 3362 (c) 6806 (d) 3321
  25. 25.What is the 29th term of the AP 14, 18, 22, 26, …? (a) 112 (b) 126 (c) 116 (d) 130
  26. 26.What is the 40th term of the AP 11, 19, 27, 35, …? (a) 323 (b) 320 (c) 312 (d) 331
  27. 27.What is the 23rd term of the AP 13, 17, 21, 25, …? (a) 105 (b) 101 (c) 92 (d) 88
  28. 28.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 18 (b) 60 (c) 50 (d) 100
  29. 29.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 13 (c) 28 (d) 56
  30. 30.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 67 (b) 408 (c) 444 (d) 816
  31. 31.Which term of the AP 16, 19, 22, 25, … is 100? (a) 28th (b) 30th (c) 31st (d) 29th
  32. 32.What is the sum of all the whole numbers from 1 to 52? (a) 1352 (b) 1326 (c) 1378 (d) 2756
  33. 33.What is the sum of all the whole numbers from 1 to 98? (a) 4802 (b) 4753 (c) 9702 (d) 4851
  34. 34.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 240 (b) 120 (c) 35 (d) 138
  35. 35.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 41 (c) 441 (d) 231
  36. 36.Which term of the AP 7, 9, 11, 13, … is 49? (a) 21st (b) 22nd (c) 23rd (d) 24th
  37. 37.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 25 (b) 170 (c) 160 (d) 320
  38. 38.What is the 37th term of the AP 12, 14, 16, 18, …? (a) 72 (b) 84 (c) 86 (d) 74
  39. 39.What is the sum of all the whole numbers from 1 to 76? (a) 5852 (b) 2888 (c) 2850 (d) 2926
  40. 40.What is the missing term in the AP 20, ?, 38, 47, 56? (a) 38 (b) 30 (c) 28 (d) 29

Answer key

  1. 200
  2. 165
  3. 86
  4. 209
  5. 161
  6. 199
  7. 91
  8. 1225
  9. 10
  10. 190
  11. 107
  12. 151
  13. 903
  14. 121
  15. 2080
  16. 130
  17. 144
  18. 528
  19. 31st
  20. 4950
  21. 666
  22. 175
  23. 92
  24. 3403
  25. 126
  26. 323
  27. 101
  28. 50
  29. 49
  30. 408
  31. 29th
  32. 1378
  33. 4851
  34. 120
  35. 441
  36. 22nd
  37. 160
  38. 84
  39. 2926
  40. 29

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