← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 559 · 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 16, ?, 28, 34, 40? (a) 22 (b) 23 (c) 28 (d) 21
  2. 2.What is the 20th term of the AP 15, 21, 27, 33, …? (a) 114 (b) 120 (c) 135 (d) 129
  3. 3.What is the 24th term of the AP 17, 19, 21, 23, …? (a) 65 (b) 46 (c) 48 (d) 63
  4. 4.What is the 29th term of the AP 8, 15, 22, 29, …? (a) 203 (b) 196 (c) 204 (d) 211
  5. 5.Which term of the AP 19, 24, 29, 34, … is 109? (a) 19th (b) 21st (c) 20th (d) 18th
  6. 6.What is the missing term in the AP 6, 9, ?, 15, 18? (a) 13 (b) 11 (c) 15 (d) 12
  7. 7.What is the 18th term of the AP 8, 16, 24, 32, …? (a) 145 (b) 152 (c) 136 (d) 144
  8. 8.What is the sum of the first 8 terms of the AP 5, 6, 7, …? (a) 12 (b) 72 (c) 136 (d) 68
  9. 9.Which term of the AP 3, 9, 15, 21, … is 57? (a) 11th (b) 12th (c) 10th (d) 9th
  10. 10.What is the 38th term of the AP 18, 25, 32, 39, …? (a) 259 (b) 284 (c) 266 (d) 277
  11. 11.What is the missing term in the AP 9, 14, 19, ?, 29? (a) 23 (b) 25 (c) 24 (d) 29
  12. 12.What is the sum of all the whole numbers from 1 to 30? (a) 930 (b) 465 (c) 435 (d) 450
  13. 13.What is the 27th term of the AP 16, 20, 24, 28, …? (a) 124 (b) 108 (c) 104 (d) 120
  14. 14.What is the sum of the first 11 terms of the AP 5, 11, 17, …? (a) 385 (b) 770 (c) 65 (d) 418
  15. 15.What is the sum of the first 7 terms of the AP 4, 6, 8, …? (a) 16 (b) 140 (c) 70 (d) 77
  16. 16.What is the 15th term of the AP 1, 7, 13, 19, …? (a) 84 (b) 90 (c) 91 (d) 85
  17. 17.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 120 (c) 29 (d) 225
  18. 18.What is the missing term in the AP 17, 26, ?, 44, 53? (a) 36 (b) 34 (c) 35 (d) 44
  19. 19.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 45 (c) 17 (d) 81
  20. 20.What is the sum of all the whole numbers from 1 to 67? (a) 2279 (b) 4556 (c) 2211 (d) 2278
  21. 21.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 57 (b) 17 (c) 114 (d) 66
  22. 22.What is the sum of the first 9 terms of the AP 3, 9, 15, …? (a) 51 (b) 486 (c) 270 (d) 243
  23. 23.What is the missing term in the AP 18, 20, 22, ?, 26? (a) 24 (b) 25 (c) 23 (d) 26
  24. 24.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 78 (c) 144 (d) 23
  25. 25.What is the 30th term of the AP 9, 15, 21, 27, …? (a) 189 (b) 183 (c) 174 (d) 180
  26. 26.What is the 13th term of the AP 13, 21, 29, 37, …? (a) 117 (b) 104 (c) 109 (d) 96
  27. 27.What is the sum of all the whole numbers from 1 to 97? (a) 4753 (b) 9506 (c) 4754 (d) 4656
  28. 28.What is the sum of the first 11 terms of the AP 7, 13, 19, …? (a) 407 (b) 440 (c) 67 (d) 814
  29. 29.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 308 (b) 46 (c) 286 (d) 572
  30. 30.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 192 (b) 96 (c) 108 (d) 26
  31. 31.What is the 33rd term of the AP 15, 18, 21, 24, …? (a) 96 (b) 99 (c) 114 (d) 111
  32. 32.What is the 35th term of the AP 7, 11, 15, 19, …? (a) 147 (b) 143 (c) 140 (d) 136
  33. 33.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 729 (c) 756 (d) 378
  34. 34.Which term of the AP 10, 15, 20, 25, … is 185? (a) 36th (b) 35th (c) 37th (d) 38th
  35. 35.What is the sum of all the whole numbers from 1 to 19? (a) 380 (b) 191 (c) 190 (d) 171
  36. 36.What is the sum of the first 7 terms of the AP 8, 11, 14, …? (a) 238 (b) 119 (c) 26 (d) 122
  37. 37.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 64 (c) 36 (d) 15
  38. 38.What is the sum of all the whole numbers from 1 to 69? (a) 4830 (b) 2346 (c) 2416 (d) 2415
  39. 39.What is the 26th term of the AP 15, 20, 25, 30, …? (a) 145 (b) 140 (c) 125 (d) 130
  40. 40.What is the missing term in the AP 20, 27, 34, ?, 48? (a) 41 (b) 42 (c) 40 (d) 48

Answer key

  1. 22
  2. 129
  3. 63
  4. 204
  5. 19th
  6. 12
  7. 144
  8. 68
  9. 10th
  10. 277
  11. 24
  12. 465
  13. 120
  14. 385
  15. 70
  16. 85
  17. 225
  18. 35
  19. 81
  20. 2278
  21. 57
  22. 243
  23. 24
  24. 144
  25. 183
  26. 109
  27. 4753
  28. 407
  29. 286
  30. 96
  31. 111
  32. 143
  33. 729
  34. 36th
  35. 190
  36. 119
  37. 64
  38. 2415
  39. 140
  40. 41

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