← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 752 · 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 12th term of the AP 14, 20, 26, 32, …? (a) 66 (b) 80 (c) 72 (d) 86
  2. 2.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 24 (b) 168 (c) 96 (d) 84
  3. 3.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 276 (c) 45 (d) 529
  4. 4.What is the 39th term of the AP 16, 19, 22, 25, …? (a) 133 (b) 130 (c) 117 (d) 114
  5. 5.What is the sum of the first 5 terms of the AP 8, 13, 18, …? (a) 180 (b) 90 (c) 95 (d) 28
  6. 6.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 36 (b) 70 (c) 35 (d) 8
  7. 7.What is the missing term in the AP 7, ?, 19, 25, 31? (a) 12 (b) 14 (c) 19 (d) 13
  8. 8.What is the sum of the first 6 terms of the AP 10, 14, 18, …? (a) 30 (b) 240 (c) 132 (d) 120
  9. 9.What is the 13th term of the AP 12, 15, 18, 21, …? (a) 48 (b) 51 (c) 36 (d) 39
  10. 10.What is the 17th term of the AP 18, 21, 24, 27, …? (a) 51 (b) 48 (c) 66 (d) 69
  11. 11.What is the sum of the first 11 terms of the AP 5, 9, 13, …? (a) 550 (b) 297 (c) 45 (d) 275
  12. 12.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 210 (c) 420 (d) 400
  13. 13.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 31 (b) 126 (c) 222 (d) 111
  14. 14.What is the sum of the first 12 terms of the AP 7, 8, 9, …? (a) 156 (b) 300 (c) 18 (d) 150
  15. 15.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 21 (c) 66 (d) 121
  16. 16.Which term of the AP 15, 17, 19, 21, … is 35? (a) 12th (b) 10th (c) 11th (d) 13th
  17. 17.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 49 (c) 625 (d) 325
  18. 18.What is the 28th term of the AP 4, 12, 20, 28, …? (a) 220 (b) 224 (c) 228 (d) 216
  19. 19.What is the missing term in the AP 20, 24, ?, 32, 36? (a) 27 (b) 28 (c) 32 (d) 29
  20. 20.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 10 (b) 41 (c) 80 (d) 40
  21. 21.What is the 30th term of the AP 17, 26, 35, 44, …? (a) 278 (b) 270 (c) 287 (d) 261
  22. 22.What is the 27th term of the AP 19, 26, 33, 40, …? (a) 208 (b) 201 (c) 189 (d) 182
  23. 23.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 324 (c) 342 (d) 35
  24. 24.What is the missing term in the AP 3, 10, ?, 24, 31? (a) 17 (b) 16 (c) 24 (d) 18
  25. 25.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 20 (b) 18 (c) 19 (d) 21
  26. 26.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 18 (b) 120 (c) 63 (d) 60
  27. 27.What is the 28th term of the AP 3, 8, 13, 18, …? (a) 140 (b) 143 (c) 135 (d) 138
  28. 28.What is the 17th term of the AP 2, 6, 10, 14, …? (a) 66 (b) 70 (c) 64 (d) 68
  29. 29.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 43 (c) 506 (d) 484
  30. 30.What is the missing term in the AP 14, 22, 30, ?, 46? (a) 39 (b) 37 (c) 46 (d) 38
  31. 31.Which term of the AP 20, 24, 28, 32, … is 120? (a) 30th (b) 27th (c) 25th (d) 26th
  32. 32.What is the sum of all the whole numbers from 1 to 10? (a) 110 (b) 45 (c) 50 (d) 55
  33. 33.What is the 14th term of the AP 1, 3, 5, 7, …? (a) 27 (b) 28 (c) 29 (d) 26
  34. 34.What is the sum of all the whole numbers from 1 to 53? (a) 1432 (b) 2862 (c) 1378 (d) 1431
  35. 35.What is the sum of the first 12 terms of the AP 5, 9, 13, …? (a) 324 (b) 648 (c) 49 (d) 348
  36. 36.What is the missing term in the AP 11, 17, 23, ?, 35? (a) 28 (b) 29 (c) 30 (d) 35
  37. 37.What is the missing term in the AP 12, 15, ?, 21, 24? (a) 17 (b) 18 (c) 21 (d) 19
  38. 38.What is the 12th term of the AP 5, 14, 23, 32, …? (a) 113 (b) 108 (c) 104 (d) 99
  39. 39.What is the 18th term of the AP 18, 26, 34, 42, …? (a) 162 (b) 154 (c) 136 (d) 144
  40. 40.What is the 30th term of the AP 8, 11, 14, 17, …? (a) 95 (b) 90 (c) 98 (d) 87

Answer key

  1. 80
  2. 84
  3. 529
  4. 130
  5. 90
  6. 35
  7. 13
  8. 120
  9. 48
  10. 66
  11. 275
  12. 400
  13. 111
  14. 150
  15. 121
  16. 11th
  17. 625
  18. 220
  19. 28
  20. 40
  21. 278
  22. 201
  23. 324
  24. 17
  25. 19
  26. 60
  27. 138
  28. 66
  29. 484
  30. 38
  31. 26th
  32. 55
  33. 27
  34. 1431
  35. 324
  36. 29
  37. 18
  38. 104
  39. 154
  40. 95

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