← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 425 · 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 sum of the first 12 terms of the AP 9, 12, 15, …? (a) 324 (b) 306 (c) 42 (d) 612
  2. 2.What is the missing term in the AP 2, 5, ?, 11, 14? (a) 7 (b) 11 (c) 8 (d) 9
  3. 3.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 17 (b) 88 (c) 160 (d) 80
  4. 4.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 14 (b) 16 (c) 13 (d) 12
  5. 5.What is the missing term in the AP 6, ?, 16, 21, 26? (a) 12 (b) 11 (c) 16 (d) 10
  6. 6.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 9 (d) 25
  7. 7.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 272 (c) 136 (d) 256
  8. 8.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 39 (c) 400 (d) 420
  9. 9.What is the missing term in the AP 6, 14, ?, 30, 38? (a) 21 (b) 23 (c) 22 (d) 30
  10. 10.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 39 (b) 210 (c) 420 (d) 230
  11. 11.What is the sum of all the whole numbers from 1 to 71? (a) 5112 (b) 2557 (c) 2485 (d) 2556
  12. 12.What is the sum of the first 8 terms of the AP 5, 10, 15, …? (a) 200 (b) 40 (c) 360 (d) 180
  13. 13.What is the 26th term of the AP 10, 18, 26, 34, …? (a) 218 (b) 210 (c) 208 (d) 200
  14. 14.What is the missing term in the AP 20, 26, 32, ?, 44? (a) 39 (b) 44 (c) 38 (d) 37
  15. 15.What is the sum of all the whole numbers from 1 to 84? (a) 7140 (b) 3528 (c) 3570 (d) 3486
  16. 16.What is the sum of the first 11 terms of the AP 10, 16, 22, …? (a) 473 (b) 880 (c) 440 (d) 70
  17. 17.What is the sum of all the whole numbers from 1 to 95? (a) 4561 (b) 4465 (c) 9120 (d) 4560
  18. 18.What is the sum of all the whole numbers from 1 to 22? (a) 253 (b) 506 (c) 242 (d) 231
  19. 19.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 360 (b) 190 (c) 180 (d) 27
  20. 20.What is the sum of all the whole numbers from 1 to 31? (a) 497 (b) 496 (c) 992 (d) 465
  21. 21.What is the sum of the first 5 terms of the AP 10, 14, 18, …? (a) 180 (b) 26 (c) 100 (d) 90
  22. 22.Which term of the AP 20, 23, 26, 29, … is 41? (a) 9th (b) 8th (c) 10th (d) 7th
  23. 23.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 784 (c) 406 (d) 812
  24. 24.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 120 (b) 105 (c) 30 (d) 210
  25. 25.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 576 (c) 47 (d) 600
  26. 26.What is the 24th term of the AP 10, 12, 14, 16, …? (a) 56 (b) 48 (c) 46 (d) 58
  27. 27.What is the missing term in the AP 13, 22, ?, 40, 49? (a) 40 (b) 31 (c) 32 (d) 30
  28. 28.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 462 (c) 441 (d) 231
  29. 29.What is the 20th term of the AP 19, 26, 33, 40, …? (a) 159 (b) 133 (c) 152 (d) 140
  30. 30.What is the sum of all the whole numbers from 1 to 53? (a) 1432 (b) 1378 (c) 1431 (d) 2862
  31. 31.What is the 17th term of the AP 6, 14, 22, 30, …? (a) 134 (b) 136 (c) 128 (d) 142
  32. 32.What is the sum of the first 6 terms of the AP 1, 4, 7, …? (a) 51 (b) 102 (c) 16 (d) 60
  33. 33.What is the sum of all the whole numbers from 1 to 29? (a) 436 (b) 870 (c) 406 (d) 435
  34. 34.What is the 14th term of the AP 13, 15, 17, 19, …? (a) 39 (b) 41 (c) 26 (d) 28
  35. 35.What is the sum of the first 5 terms of the AP 7, 9, 11, …? (a) 15 (b) 60 (c) 55 (d) 110
  36. 36.What is the missing term in the AP 14, 17, 20, ?, 26? (a) 22 (b) 24 (c) 23 (d) 26
  37. 37.What is the 36th term of the AP 5, 10, 15, 20, …? (a) 181 (b) 185 (c) 175 (d) 180
  38. 38.What is the sum of the first 7 terms of the AP 5, 11, 17, …? (a) 322 (b) 161 (c) 41 (d) 182
  39. 39.What is the 16th term of the AP 16, 23, 30, 37, …? (a) 105 (b) 112 (c) 121 (d) 128
  40. 40.What is the 14th term of the AP 19, 25, 31, 37, …? (a) 84 (b) 78 (c) 103 (d) 97

Answer key

  1. 306
  2. 8
  3. 80
  4. 13
  5. 11
  6. 25
  7. 256
  8. 400
  9. 22
  10. 210
  11. 2556
  12. 180
  13. 210
  14. 38
  15. 3570
  16. 440
  17. 4560
  18. 253
  19. 180
  20. 496
  21. 90
  22. 8th
  23. 784
  24. 105
  25. 576
  26. 56
  27. 31
  28. 441
  29. 152
  30. 1431
  31. 134
  32. 51
  33. 435
  34. 39
  35. 55
  36. 23
  37. 180
  38. 161
  39. 121
  40. 97

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