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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 910 · 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 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 41 (c) 441 (d) 231
  2. 2.What is the missing term in the AP 10, 19, 28, ?, 46? (a) 36 (b) 37 (c) 38 (d) 46
  3. 3.What is the sum of all the whole numbers from 1 to 86? (a) 3698 (b) 3655 (c) 7482 (d) 3741
  4. 4.What is the 18th term of the AP 12, 15, 18, 21, …? (a) 66 (b) 51 (c) 54 (d) 63
  5. 5.What is the sum of the first 12 terms of the AP 3, 5, 7, …? (a) 180 (b) 336 (c) 25 (d) 168
  6. 6.What is the missing term in the AP 2, ?, 16, 23, 30? (a) 8 (b) 16 (c) 9 (d) 10
  7. 7.What is the sum of all the whole numbers from 1 to 34? (a) 1190 (b) 595 (c) 561 (d) 578
  8. 8.What is the sum of the first 9 terms of the AP 1, 4, 7, …? (a) 25 (b) 234 (c) 117 (d) 120
  9. 9.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 300 (c) 600 (d) 47
  10. 10.Which term of the AP 19, 21, 23, 25, … is 69? (a) 27th (b) 26th (c) 28th (d) 25th
  11. 11.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 28 (c) 56 (d) 13
  12. 12.What is the sum of the first 10 terms of the AP 7, 12, 17, …? (a) 590 (b) 320 (c) 52 (d) 295
  13. 13.What is the 39th term of the AP 3, 9, 15, 21, …? (a) 234 (b) 231 (c) 228 (d) 237
  14. 14.What is the 21st term of the AP 3, 10, 17, 24, …? (a) 143 (b) 140 (c) 147 (d) 150
  15. 15.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 23 (c) 78 (d) 156
  16. 16.What is the 32nd term of the AP 13, 15, 17, 19, …? (a) 64 (b) 77 (c) 75 (d) 62
  17. 17.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 15 (b) 126 (c) 70 (d) 63
  18. 18.Which term of the AP 17, 20, 23, 26, … is 131? (a) 40th (b) 38th (c) 39th (d) 41st
  19. 19.What is the 26th term of the AP 10, 17, 24, 31, …? (a) 182 (b) 185 (c) 175 (d) 192
  20. 20.What is the 31st term of the AP 15, 21, 27, 33, …? (a) 180 (b) 186 (c) 201 (d) 195
  21. 21.What is the 26th term of the AP 3, 6, 9, 12, …? (a) 75 (b) 81 (c) 78 (d) 79
  22. 22.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 676 (c) 351 (d) 51
  23. 23.Which term of the AP 11, 20, 29, 38, … is 281? (a) 32nd (b) 33rd (c) 31st (d) 30th
  24. 24.What is the sum of the first 10 terms of the AP 2, 6, 10, …? (a) 400 (b) 200 (c) 38 (d) 220
  25. 25.What is the 20th term of the AP 5, 8, 11, 14, …? (a) 65 (b) 57 (c) 60 (d) 62
  26. 26.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 100 (c) 19 (d) 55
  27. 27.What is the 15th term of the AP 14, 16, 18, 20, …? (a) 30 (b) 42 (c) 28 (d) 44
  28. 28.What is the sum of the first 7 terms of the AP 3, 6, 9, …? (a) 84 (b) 87 (c) 21 (d) 168
  29. 29.What is the sum of all the whole numbers from 1 to 43? (a) 1892 (b) 947 (c) 903 (d) 946
  30. 30.What is the 30th term of the AP 4, 9, 14, 19, …? (a) 149 (b) 145 (c) 150 (d) 154
  31. 31.What is the 34th term of the AP 8, 13, 18, 23, …? (a) 173 (b) 178 (c) 165 (d) 170
  32. 32.What is the sum of all the whole numbers from 1 to 65? (a) 4290 (b) 2145 (c) 2146 (d) 2080
  33. 33.Which term of the AP 5, 10, 15, 20, … is 160? (a) 31st (b) 34th (c) 32nd (d) 33rd
  34. 34.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 352 (b) 176 (c) 26 (d) 187
  35. 35.What is the 38th term of the AP 2, 9, 16, 23, …? (a) 261 (b) 266 (c) 259 (d) 268
  36. 36.What is the 28th term of the AP 6, 8, 10, 12, …? (a) 56 (b) 54 (c) 60 (d) 62
  37. 37.What is the 39th term of the AP 20, 23, 26, 29, …? (a) 137 (b) 114 (c) 134 (d) 117
  38. 38.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 160 (b) 320 (c) 170 (d) 25
  39. 39.What is the 14th term of the AP 8, 12, 16, 20, …? (a) 60 (b) 52 (c) 56 (d) 64
  40. 40.What is the sum of the first 12 terms of the AP 2, 5, 8, …? (a) 35 (b) 222 (c) 240 (d) 444

Answer key

  1. 441
  2. 37
  3. 3741
  4. 63
  5. 168
  6. 9
  7. 595
  8. 117
  9. 576
  10. 26th
  11. 49
  12. 295
  13. 231
  14. 143
  15. 144
  16. 75
  17. 63
  18. 39th
  19. 185
  20. 195
  21. 78
  22. 676
  23. 31st
  24. 200
  25. 62
  26. 100
  27. 42
  28. 84
  29. 946
  30. 149
  31. 173
  32. 2145
  33. 32nd
  34. 176
  35. 261
  36. 60
  37. 134
  38. 160
  39. 60
  40. 222

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