← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 249 · 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 17th term of the AP 20, 22, 24, 26, …? (a) 32 (b) 34 (c) 54 (d) 52
  2. 2.Which term of the AP 11, 20, 29, 38, … is 218? (a) 24th (b) 23rd (c) 25th (d) 26th
  3. 3.What is the 35th term of the AP 13, 19, 25, 31, …? (a) 204 (b) 210 (c) 223 (d) 217
  4. 4.What is the sum of the first 12 terms of the AP 10, 14, 18, …? (a) 768 (b) 408 (c) 54 (d) 384
  5. 5.Which term of the AP 8, 14, 20, 26, … is 176? (a) 29th (b) 28th (c) 30th (d) 31st
  6. 6.What is the missing term in the AP 10, 18, ?, 34, 42? (a) 25 (b) 26 (c) 27 (d) 34
  7. 7.What is the sum of the first 6 terms of the AP 6, 12, 18, …? (a) 144 (b) 126 (c) 252 (d) 36
  8. 8.What is the 13th term of the AP 3, 11, 19, 27, …? (a) 96 (b) 107 (c) 99 (d) 104
  9. 9.What is the sum of the first 9 terms of the AP 5, 9, 13, …? (a) 37 (b) 207 (c) 378 (d) 189
  10. 10.What is the 15th term of the AP 6, 14, 22, 30, …? (a) 126 (b) 112 (c) 118 (d) 120
  11. 11.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 190 (c) 380 (d) 361
  12. 12.What is the missing term in the AP 10, 15, 20, ?, 30? (a) 25 (b) 24 (c) 30 (d) 26
  13. 13.What is the missing term in the AP 14, ?, 26, 32, 38? (a) 26 (b) 19 (c) 20 (d) 21
  14. 14.What is the 39th term of the AP 16, 18, 20, 22, …? (a) 78 (b) 76 (c) 92 (d) 94
  15. 15.What is the sum of the first 8 terms of the AP 6, 7, 8, …? (a) 13 (b) 80 (c) 76 (d) 152
  16. 16.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 80 (b) 150 (c) 75 (d) 12
  17. 17.What is the 33rd term of the AP 9, 15, 21, 27, …? (a) 198 (b) 201 (c) 192 (d) 207
  18. 18.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 120 (b) 21 (c) 112 (d) 224
  19. 19.Which term of the AP 8, 15, 22, 29, … is 239? (a) 36th (b) 33rd (c) 35th (d) 34th
  20. 20.What is the 14th term of the AP 12, 19, 26, 33, …? (a) 98 (b) 103 (c) 91 (d) 110
  21. 21.What is the 33rd term of the AP 6, 10, 14, 18, …? (a) 138 (b) 134 (c) 128 (d) 132
  22. 22.What is the 32nd term of the AP 1, 7, 13, 19, …? (a) 187 (b) 192 (c) 193 (d) 186
  23. 23.Which term of the AP 6, 12, 18, 24, … is 204? (a) 35th (b) 36th (c) 33rd (d) 34th
  24. 24.What is the sum of the first 11 terms of the AP 6, 9, 12, …? (a) 231 (b) 462 (c) 234 (d) 36
  25. 25.Which term of the AP 16, 24, 32, 40, … is 240? (a) 29th (b) 31st (c) 28th (d) 30th
  26. 26.What is the sum of the first 8 terms of the AP 8, 12, 16, …? (a) 192 (b) 36 (c) 176 (d) 352
  27. 27.Which term of the AP 14, 21, 28, 35, … is 217? (a) 31st (b) 29th (c) 32nd (d) 30th
  28. 28.Which term of the AP 8, 16, 24, 32, … is 176? (a) 22nd (b) 21st (c) 23rd (d) 24th
  29. 29.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 342 (c) 324 (d) 171
  30. 30.What is the 25th term of the AP 18, 20, 22, 24, …? (a) 50 (b) 68 (c) 48 (d) 66
  31. 31.What is the missing term in the AP 2, 10, ?, 26, 34? (a) 18 (b) 17 (c) 26 (d) 19
  32. 32.What is the sum of all the whole numbers from 1 to 52? (a) 1352 (b) 1326 (c) 2756 (d) 1378
  33. 33.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 25 (b) 80 (c) 130 (d) 65
  34. 34.Which term of the AP 2, 5, 8, 11, … is 116? (a) 39th (b) 38th (c) 41st (d) 40th
  35. 35.What is the 15th term of the AP 12, 15, 18, 21, …? (a) 57 (b) 42 (c) 54 (d) 45
  36. 36.What is the 10th term of the AP 7, 10, 13, 16, …? (a) 37 (b) 34 (c) 30 (d) 27
  37. 37.What is the missing term in the AP 9, ?, 25, 33, 41? (a) 17 (b) 25 (c) 18 (d) 16
  38. 38.Which term of the AP 6, 8, 10, 12, … is 84? (a) 40th (b) 41st (c) 42nd (d) 39th
  39. 39.What is the missing term in the AP 12, ?, 24, 30, 36? (a) 17 (b) 19 (c) 18 (d) 24
  40. 40.What is the 11th term of the AP 8, 12, 16, 20, …? (a) 48 (b) 52 (c) 44 (d) 40

Answer key

  1. 52
  2. 24th
  3. 217
  4. 384
  5. 29th
  6. 26
  7. 126
  8. 99
  9. 189
  10. 118
  11. 361
  12. 25
  13. 20
  14. 92
  15. 76
  16. 75
  17. 201
  18. 112
  19. 34th
  20. 103
  21. 134
  22. 187
  23. 34th
  24. 231
  25. 29th
  26. 176
  27. 30th
  28. 22nd
  29. 324
  30. 66
  31. 18
  32. 1378
  33. 65
  34. 39th
  35. 54
  36. 34
  37. 17
  38. 40th
  39. 18
  40. 48

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