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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 197 · 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 10, 14, 18, …? (a) 168 (b) 154 (c) 308 (d) 34
  2. 2.What is the sum of all the whole numbers from 1 to 57? (a) 1654 (b) 3306 (c) 1653 (d) 1596
  3. 3.What is the missing term in the AP 2, ?, 18, 26, 34? (a) 11 (b) 9 (c) 18 (d) 10
  4. 4.What is the 34th term of the AP 19, 25, 31, 37, …? (a) 217 (b) 198 (c) 204 (d) 223
  5. 5.What is the sum of the first 6 terms of the AP 8, 10, 12, …? (a) 78 (b) 156 (c) 84 (d) 18
  6. 6.Which term of the AP 6, 14, 22, 30, … is 294? (a) 38th (b) 39th (c) 36th (d) 37th
  7. 7.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 465 (c) 930 (d) 900
  8. 8.What is the 18th term of the AP 14, 17, 20, 23, …? (a) 51 (b) 65 (c) 54 (d) 68
  9. 9.What is the 17th term of the AP 20, 28, 36, 44, …? (a) 128 (b) 148 (c) 136 (d) 156
  10. 10.What is the 23rd term of the AP 1, 3, 5, 7, …? (a) 47 (b) 44 (c) 45 (d) 46
  11. 11.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 120 (c) 29 (d) 225
  12. 12.What is the 29th term of the AP 13, 17, 21, 25, …? (a) 129 (b) 116 (c) 125 (d) 112
  13. 13.What is the missing term in the AP 10, 13, 16, ?, 22? (a) 20 (b) 22 (c) 18 (d) 19
  14. 14.What is the sum of all the whole numbers from 1 to 87? (a) 3828 (b) 7656 (c) 3741 (d) 3829
  15. 15.Which term of the AP 16, 25, 34, 43, … is 313? (a) 35th (b) 34th (c) 33rd (d) 36th
  16. 16.What is the 33rd term of the AP 11, 20, 29, 38, …? (a) 288 (b) 308 (c) 299 (d) 297
  17. 17.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 25 (b) 105 (c) 210 (d) 114
  18. 18.What is the 33rd term of the AP 4, 8, 12, 16, …? (a) 133 (b) 136 (c) 128 (d) 132
  19. 19.What is the 38th term of the AP 3, 6, 9, 12, …? (a) 114 (b) 111 (c) 115 (d) 117
  20. 20.What is the 13th term of the AP 11, 19, 27, 35, …? (a) 107 (b) 115 (c) 96 (d) 104
  21. 21.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 100 (d) 110
  22. 22.What is the sum of the first 6 terms of the AP 6, 12, 18, …? (a) 252 (b) 144 (c) 36 (d) 126
  23. 23.Which term of the AP 3, 12, 21, 30, … is 273? (a) 32nd (b) 30th (c) 31st (d) 33rd
  24. 24.What is the 24th term of the AP 3, 12, 21, 30, …? (a) 207 (b) 219 (c) 210 (d) 216
  25. 25.What is the 11th term of the AP 9, 12, 15, 18, …? (a) 42 (b) 33 (c) 30 (d) 39
  26. 26.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 200 (b) 32 (c) 370 (d) 185
  27. 27.What is the sum of all the whole numbers from 1 to 45? (a) 1035 (b) 1036 (c) 2070 (d) 990
  28. 28.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 12 (b) 51 (c) 100 (d) 50
  29. 29.What is the sum of all the whole numbers from 1 to 44? (a) 1980 (b) 946 (c) 968 (d) 990
  30. 30.What is the sum of all the whole numbers from 1 to 71? (a) 5112 (b) 2557 (c) 2485 (d) 2556
  31. 31.What is the sum of the first 8 terms of the AP 10, 15, 20, …? (a) 440 (b) 45 (c) 220 (d) 240
  32. 32.What is the 31st term of the AP 7, 11, 15, 19, …? (a) 127 (b) 124 (c) 131 (d) 120
  33. 33.What is the sum of the first 12 terms of the AP 4, 8, 12, …? (a) 48 (b) 336 (c) 624 (d) 312
  34. 34.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 676 (c) 351 (d) 51
  35. 35.What is the 40th term of the AP 14, 16, 18, 20, …? (a) 94 (b) 80 (c) 92 (d) 78
  36. 36.What is the sum of the first 7 terms of the AP 3, 7, 11, …? (a) 27 (b) 119 (c) 105 (d) 210
  37. 37.What is the 36th term of the AP 12, 16, 20, 24, …? (a) 144 (b) 152 (c) 140 (d) 156
  38. 38.What is the missing term in the AP 19, ?, 33, 40, 47? (a) 25 (b) 27 (c) 33 (d) 26
  39. 39.What is the sum of all the whole numbers from 1 to 52? (a) 1326 (b) 1378 (c) 1352 (d) 2756
  40. 40.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 496 (c) 497 (d) 992

Answer key

  1. 154
  2. 1653
  3. 10
  4. 217
  5. 78
  6. 37th
  7. 900
  8. 65
  9. 148
  10. 45
  11. 225
  12. 125
  13. 19
  14. 3828
  15. 34th
  16. 299
  17. 105
  18. 132
  19. 114
  20. 107
  21. 100
  22. 126
  23. 31st
  24. 210
  25. 39
  26. 185
  27. 1035
  28. 50
  29. 990
  30. 2556
  31. 220
  32. 127
  33. 312
  34. 676
  35. 92
  36. 105
  37. 152
  38. 26
  39. 1378
  40. 496

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