← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 394 · 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.Which term of the AP 20, 23, 26, 29, … is 137? (a) 40th (b) 41st (c) 42nd (d) 39th
  2. 2.What is the missing term in the AP 18, 23, ?, 33, 38? (a) 28 (b) 29 (c) 27 (d) 33
  3. 3.Which term of the AP 12, 15, 18, 21, … is 111? (a) 37th (b) 34th (c) 35th (d) 33rd
  4. 4.What is the 17th term of the AP 14, 17, 20, 23, …? (a) 62 (b) 65 (c) 51 (d) 48
  5. 5.What is the sum of all the whole numbers from 1 to 66? (a) 4422 (b) 2178 (c) 2145 (d) 2211
  6. 6.What is the sum of all the whole numbers from 1 to 76? (a) 5852 (b) 2850 (c) 2888 (d) 2926
  7. 7.What is the 10th term of the AP 5, 7, 9, 11, …? (a) 23 (b) 20 (c) 18 (d) 25
  8. 8.Which term of the AP 3, 12, 21, 30, … is 120? (a) 14th (b) 16th (c) 13th (d) 15th
  9. 9.What is the 33rd term of the AP 2, 11, 20, 29, …? (a) 290 (b) 299 (c) 297 (d) 288
  10. 10.Which term of the AP 10, 19, 28, 37, … is 307? (a) 36th (b) 35th (c) 33rd (d) 34th
  11. 11.What is the missing term in the AP 16, ?, 28, 34, 40? (a) 28 (b) 23 (c) 21 (d) 22
  12. 12.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 60 (b) 120 (c) 63 (d) 18
  13. 13.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 110 (b) 56 (c) 55 (d) 13
  14. 14.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 225 (c) 120 (d) 29
  15. 15.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 75 (b) 15 (c) 150 (d) 78
  16. 16.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 756 (c) 729 (d) 53
  17. 17.What is the 26th term of the AP 9, 13, 17, 21, …? (a) 113 (b) 104 (c) 109 (d) 100
  18. 18.What is the 20th term of the AP 18, 21, 24, 27, …? (a) 57 (b) 60 (c) 75 (d) 78
  19. 19.What is the 10th term of the AP 12, 18, 24, 30, …? (a) 72 (b) 54 (c) 66 (d) 60
  20. 20.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 122 (b) 121 (c) 16 (d) 242
  21. 21.What is the 34th term of the AP 2, 10, 18, 26, …? (a) 272 (b) 274 (c) 264 (d) 266
  22. 22.What is the sum of the first 11 terms of the AP 7, 8, 9, …? (a) 17 (b) 132 (c) 264 (d) 133
  23. 23.What is the 28th term of the AP 8, 11, 14, 17, …? (a) 89 (b) 84 (c) 92 (d) 81
  24. 24.What is the sum of the first 7 terms of the AP 6, 8, 10, …? (a) 84 (b) 91 (c) 18 (d) 168
  25. 25.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 53 (b) 100 (c) 16 (d) 50
  26. 26.What is the missing term in the AP 14, 16, 18, ?, 22? (a) 19 (b) 22 (c) 21 (d) 20
  27. 27.What is the sum of the first 10 terms of the AP 4, 6, 8, …? (a) 140 (b) 130 (c) 260 (d) 22
  28. 28.What is the 23rd term of the AP 13, 22, 31, 40, …? (a) 198 (b) 207 (c) 220 (d) 211
  29. 29.What is the sum of the first 7 terms of the AP 6, 7, 8, …? (a) 63 (b) 12 (c) 126 (d) 64
  30. 30.What is the sum of all the whole numbers from 1 to 42? (a) 1806 (b) 903 (c) 861 (d) 882
  31. 31.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 72 (c) 15 (d) 36
  32. 32.Which term of the AP 2, 11, 20, 29, … is 272? (a) 31st (b) 30th (c) 33rd (d) 32nd
  33. 33.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 57 (c) 435 (d) 870
  34. 34.What is the 35th term of the AP 6, 8, 10, 12, …? (a) 68 (b) 74 (c) 70 (d) 76
  35. 35.What is the sum of all the whole numbers from 1 to 68? (a) 2312 (b) 2278 (c) 2346 (d) 4692
  36. 36.What is the sum of the first 8 terms of the AP 7, 10, 13, …? (a) 28 (b) 280 (c) 152 (d) 140
  37. 37.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 21 (c) 132 (d) 121
  38. 38.What is the 14th term of the AP 16, 22, 28, 34, …? (a) 78 (b) 94 (c) 100 (d) 84
  39. 39.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 136 (c) 256 (d) 272
  40. 40.What is the 29th term of the AP 4, 6, 8, 10, …? (a) 56 (b) 58 (c) 60 (d) 62

Answer key

  1. 40th
  2. 28
  3. 34th
  4. 62
  5. 2211
  6. 2926
  7. 23
  8. 14th
  9. 290
  10. 34th
  11. 22
  12. 60
  13. 55
  14. 225
  15. 75
  16. 729
  17. 109
  18. 75
  19. 66
  20. 121
  21. 266
  22. 132
  23. 89
  24. 84
  25. 50
  26. 20
  27. 130
  28. 211
  29. 63
  30. 903
  31. 64
  32. 31st
  33. 841
  34. 74
  35. 2346
  36. 140
  37. 121
  38. 94
  39. 256
  40. 60

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad