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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 727 · 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 31st term of the AP 6, 9, 12, 15, …? (a) 93 (b) 99 (c) 96 (d) 90
  2. 2.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 176 (b) 88 (c) 18 (d) 96
  3. 3.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 441 (c) 462 (d) 41
  4. 4.What is the 33rd term of the AP 11, 15, 19, 23, …? (a) 143 (b) 128 (c) 132 (d) 139
  5. 5.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 435 (c) 870 (d) 57
  6. 6.What is the 38th term of the AP 4, 6, 8, 10, …? (a) 80 (b) 74 (c) 76 (d) 78
  7. 7.What is the sum of the first 6 terms of the AP 5, 7, 9, …? (a) 120 (b) 66 (c) 60 (d) 15
  8. 8.What is the sum of all the whole numbers from 1 to 10? (a) 110 (b) 45 (c) 55 (d) 50
  9. 9.Which term of the AP 3, 11, 19, 27, … is 91? (a) 11th (b) 14th (c) 12th (d) 13th
  10. 10.What is the 37th term of the AP 17, 26, 35, 44, …? (a) 350 (b) 324 (c) 341 (d) 333
  11. 11.What is the 36th term of the AP 1, 8, 15, 22, …? (a) 245 (b) 253 (c) 246 (d) 252
  12. 12.What is the sum of all the whole numbers from 1 to 53? (a) 2862 (b) 1431 (c) 1432 (d) 1378
  13. 13.What is the 32nd term of the AP 3, 11, 19, 27, …? (a) 256 (b) 259 (c) 248 (d) 251
  14. 14.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 11 (b) 40 (c) 70 (d) 35
  15. 15.What is the 12th term of the AP 18, 21, 24, 27, …? (a) 33 (b) 51 (c) 54 (d) 36
  16. 16.What is the sum of the first 10 terms of the AP 9, 14, 19, …? (a) 340 (b) 315 (c) 630 (d) 54
  17. 17.What is the 20th term of the AP 7, 13, 19, 25, …? (a) 120 (b) 114 (c) 121 (d) 127
  18. 18.Which term of the AP 20, 22, 24, 26, … is 48? (a) 24th (b) 16th (c) 15th (d) 14th
  19. 19.What is the 16th term of the AP 19, 28, 37, 46, …? (a) 135 (b) 163 (c) 144 (d) 154
  20. 20.What is the missing term in the AP 8, 10, ?, 14, 16? (a) 13 (b) 11 (c) 14 (d) 12
  21. 21.What is the 29th term of the AP 7, 10, 13, 16, …? (a) 94 (b) 84 (c) 91 (d) 87
  22. 22.What is the 23rd term of the AP 3, 7, 11, 15, …? (a) 91 (b) 92 (c) 88 (d) 95
  23. 23.Which term of the AP 14, 16, 18, 20, … is 92? (a) 41st (b) 39th (c) 46th (d) 40th
  24. 24.What is the sum of the first 8 terms of the AP 5, 6, 7, …? (a) 72 (b) 12 (c) 68 (d) 136
  25. 25.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 45 (c) 529 (d) 552
  26. 26.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 222 (b) 31 (c) 126 (d) 111
  27. 27.What is the missing term in the AP 5, 9, 13, ?, 21? (a) 21 (b) 18 (c) 16 (d) 17
  28. 28.Which term of the AP 10, 13, 16, 19, … is 124? (a) 40th (b) 41st (c) 39th (d) 38th
  29. 29.What is the sum of all the whole numbers from 1 to 30? (a) 930 (b) 450 (c) 435 (d) 465
  30. 30.What is the missing term in the AP 8, 16, ?, 32, 40? (a) 25 (b) 24 (c) 23 (d) 32
  31. 31.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 66 (c) 21 (d) 132
  32. 32.What is the sum of all the whole numbers from 1 to 70? (a) 2415 (b) 2450 (c) 4970 (d) 2485
  33. 33.What is the missing term in the AP 17, 23, ?, 35, 41? (a) 29 (b) 35 (c) 28 (d) 30
  34. 34.What is the 11th term of the AP 7, 10, 13, 16, …? (a) 30 (b) 37 (c) 40 (d) 33
  35. 35.What is the 39th term of the AP 15, 18, 21, 24, …? (a) 132 (b) 114 (c) 117 (d) 129
  36. 36.What is the sum of the first 5 terms of the AP 9, 14, 19, …? (a) 100 (b) 95 (c) 190 (d) 29
  37. 37.What is the 39th term of the AP 11, 14, 17, 20, …? (a) 125 (b) 114 (c) 128 (d) 117
  38. 38.Which term of the AP 17, 23, 29, 35, … is 95? (a) 14th (b) 13th (c) 15th (d) 16th
  39. 39.What is the sum of all the whole numbers from 1 to 34? (a) 578 (b) 561 (c) 595 (d) 1190
  40. 40.What is the 16th term of the AP 19, 27, 35, 43, …? (a) 147 (b) 128 (c) 139 (d) 120

Answer key

  1. 96
  2. 88
  3. 441
  4. 139
  5. 841
  6. 78
  7. 60
  8. 55
  9. 12th
  10. 341
  11. 246
  12. 1431
  13. 251
  14. 35
  15. 51
  16. 315
  17. 121
  18. 15th
  19. 154
  20. 12
  21. 91
  22. 91
  23. 40th
  24. 68
  25. 529
  26. 111
  27. 17
  28. 39th
  29. 465
  30. 24
  31. 121
  32. 2485
  33. 29
  34. 37
  35. 129
  36. 95
  37. 125
  38. 14th
  39. 595
  40. 139

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