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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 678 · 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 missing term in the AP 15, 23, 31, ?, 47? (a) 39 (b) 38 (c) 40 (d) 47
  2. 2.What is the 10th term of the AP 1, 5, 9, 13, …? (a) 40 (b) 41 (c) 36 (d) 37
  3. 3.What is the missing term in the AP 12, 18, ?, 30, 36? (a) 25 (b) 30 (c) 23 (d) 24
  4. 4.Which term of the AP 15, 24, 33, 42, … is 303? (a) 32nd (b) 33rd (c) 34th (d) 35th
  5. 5.What is the 26th term of the AP 12, 20, 28, 36, …? (a) 200 (b) 212 (c) 208 (d) 220
  6. 6.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 256 (c) 272 (d) 136
  7. 7.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 100 (c) 19 (d) 110
  8. 8.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 264 (b) 504 (c) 252 (d) 32
  9. 9.Which term of the AP 7, 11, 15, 19, … is 47? (a) 12th (b) 13th (c) 10th (d) 11th
  10. 10.What is the sum of all the whole numbers from 1 to 81? (a) 3321 (b) 6642 (c) 3322 (d) 3240
  11. 11.What is the 34th term of the AP 9, 14, 19, 24, …? (a) 165 (b) 179 (c) 170 (d) 174
  12. 12.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 462 (c) 441 (d) 41
  13. 13.What is the 13th term of the AP 16, 22, 28, 34, …? (a) 78 (b) 72 (c) 88 (d) 94
  14. 14.What is the 14th term of the AP 16, 18, 20, 22, …? (a) 28 (b) 42 (c) 26 (d) 44
  15. 15.What is the sum of the first 11 terms of the AP 10, 13, 16, …? (a) 275 (b) 550 (c) 278 (d) 40
  16. 16.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 156 (c) 78 (d) 144
  17. 17.Which term of the AP 6, 12, 18, 24, … is 156? (a) 25th (b) 28th (c) 26th (d) 27th
  18. 18.What is the missing term in the AP 20, 24, 28, ?, 36? (a) 32 (b) 33 (c) 31 (d) 36
  19. 19.What is the missing term in the AP 17, ?, 35, 44, 53? (a) 35 (b) 27 (c) 25 (d) 26
  20. 20.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 126 (b) 70 (c) 15 (d) 63
  21. 21.What is the 17th term of the AP 11, 15, 19, 23, …? (a) 68 (b) 64 (c) 75 (d) 79
  22. 22.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 190 (c) 380 (d) 37
  23. 23.What is the missing term in the AP 14, 21, 28, ?, 42? (a) 42 (b) 36 (c) 35 (d) 34
  24. 24.Which term of the AP 12, 21, 30, 39, … is 84? (a) 9th (b) 10th (c) 8th (d) 11th
  25. 25.What is the missing term in the AP 13, 22, 31, ?, 49? (a) 39 (b) 41 (c) 40 (d) 49
  26. 26.What is the 14th term of the AP 14, 16, 18, 20, …? (a) 40 (b) 26 (c) 42 (d) 28
  27. 27.What is the sum of the first 5 terms of the AP 8, 13, 18, …? (a) 180 (b) 28 (c) 95 (d) 90
  28. 28.What is the sum of the first 10 terms of the AP 4, 10, 16, …? (a) 340 (b) 620 (c) 58 (d) 310
  29. 29.What is the 32nd term of the AP 18, 23, 28, 33, …? (a) 160 (b) 173 (c) 155 (d) 178
  30. 30.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 650 (c) 625 (d) 49
  31. 31.What is the 18th term of the AP 7, 16, 25, 34, …? (a) 160 (b) 169 (c) 153 (d) 162
  32. 32.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 25 (c) 30 (d) 15
  33. 33.What is the sum of the first 9 terms of the AP 5, 11, 17, …? (a) 522 (b) 261 (c) 288 (d) 53
  34. 34.What is the sum of all the whole numbers from 1 to 54? (a) 1458 (b) 1431 (c) 2970 (d) 1485
  35. 35.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 66 (c) 121 (d) 21
  36. 36.Which term of the AP 20, 24, 28, 32, … is 164? (a) 38th (b) 36th (c) 41st (d) 37th
  37. 37.Which term of the AP 3, 7, 11, 15, … is 119? (a) 30th (b) 29th (c) 32nd (d) 31st
  38. 38.What is the sum of the first 10 terms of the AP 10, 13, 16, …? (a) 37 (b) 470 (c) 250 (d) 235
  39. 39.What is the 12th term of the AP 9, 12, 15, 18, …? (a) 45 (b) 42 (c) 33 (d) 36
  40. 40.What is the missing term in the AP 2, 9, ?, 23, 30? (a) 15 (b) 17 (c) 23 (d) 16

Answer key

  1. 39
  2. 37
  3. 24
  4. 33rd
  5. 212
  6. 256
  7. 100
  8. 252
  9. 11th
  10. 3321
  11. 174
  12. 441
  13. 88
  14. 42
  15. 275
  16. 144
  17. 26th
  18. 32
  19. 26
  20. 63
  21. 75
  22. 361
  23. 35
  24. 9th
  25. 40
  26. 40
  27. 90
  28. 310
  29. 173
  30. 625
  31. 160
  32. 25
  33. 261
  34. 1485
  35. 121
  36. 37th
  37. 30th
  38. 235
  39. 42
  40. 16

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