← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 845 · 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 36th term of the AP 1, 8, 15, 22, …? (a) 253 (b) 245 (c) 252 (d) 246
  2. 2.What is the sum of all the whole numbers from 1 to 40? (a) 820 (b) 780 (c) 1640 (d) 800
  3. 3.What is the sum of the first 10 terms of the AP 9, 14, 19, …? (a) 54 (b) 315 (c) 630 (d) 340
  4. 4.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 17 (c) 45 (d) 90
  5. 5.What is the 14th term of the AP 6, 12, 18, 24, …? (a) 85 (b) 84 (c) 78 (d) 90
  6. 6.What is the 38th term of the AP 14, 17, 20, 23, …? (a) 114 (b) 125 (c) 111 (d) 128
  7. 7.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 222 (b) 111 (c) 126 (d) 31
  8. 8.What is the sum of all the whole numbers from 1 to 53? (a) 1431 (b) 2862 (c) 1378 (d) 1432
  9. 9.What is the 15th term of the AP 1, 3, 5, 7, …? (a) 30 (b) 28 (c) 31 (d) 29
  10. 10.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 50 (b) 18 (c) 100 (d) 60
  11. 11.What is the missing term in the AP 2, 5, 8, ?, 14? (a) 14 (b) 11 (c) 12 (d) 10
  12. 12.What is the sum of all the whole numbers from 1 to 54? (a) 2970 (b) 1431 (c) 1485 (d) 1458
  13. 13.What is the missing term in the AP 1, 9, 17, ?, 33? (a) 33 (b) 24 (c) 26 (d) 25
  14. 14.What is the sum of all the whole numbers from 1 to 43? (a) 1892 (b) 947 (c) 903 (d) 946
  15. 15.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 15 (b) 220 (c) 110 (d) 111
  16. 16.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 50 (b) 25 (c) 9 (d) 30
  17. 17.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 792 (b) 66 (c) 429 (d) 396
  18. 18.What is the missing term in the AP 11, 18, 25, ?, 39? (a) 32 (b) 33 (c) 39 (d) 31
  19. 19.What is the 16th term of the AP 20, 25, 30, 35, …? (a) 80 (b) 100 (c) 95 (d) 75
  20. 20.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 361 (c) 37 (d) 190
  21. 21.What is the 24th term of the AP 10, 19, 28, 37, …? (a) 207 (b) 216 (c) 226 (d) 217
  22. 22.What is the sum of the first 10 terms of the AP 6, 8, 10, …? (a) 24 (b) 300 (c) 160 (d) 150
  23. 23.Which term of the AP 6, 8, 10, 12, … is 34? (a) 16th (b) 17th (c) 15th (d) 14th
  24. 24.What is the sum of the first 10 terms of the AP 8, 9, 10, …? (a) 250 (b) 17 (c) 130 (d) 125
  25. 25.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 600 (d) 576
  26. 26.What is the missing term in the AP 4, ?, 14, 19, 24? (a) 8 (b) 14 (c) 10 (d) 9
  27. 27.What is the sum of the first 11 terms of the AP 10, 16, 22, …? (a) 473 (b) 70 (c) 440 (d) 880
  28. 28.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 384 (b) 216 (c) 45 (d) 192
  29. 29.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 18 (b) 176 (c) 96 (d) 88
  30. 30.What is the 40th term of the AP 2, 5, 8, 11, …? (a) 117 (b) 120 (c) 122 (d) 119
  31. 31.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 15 (c) 30 (d) 25
  32. 32.What is the 12th term of the AP 17, 24, 31, 38, …? (a) 77 (b) 84 (c) 94 (d) 101
  33. 33.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 73 (b) 12 (c) 144 (d) 72
  34. 34.What is the sum of the first 10 terms of the AP 7, 13, 19, …? (a) 370 (b) 340 (c) 680 (d) 61
  35. 35.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 9 (b) 39 (c) 42 (d) 78
  36. 36.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 462 (c) 441 (d) 41
  37. 37.What is the 38th term of the AP 10, 15, 20, 25, …? (a) 185 (b) 200 (c) 195 (d) 190
  38. 38.What is the 23rd term of the AP 4, 6, 8, 10, …? (a) 50 (b) 48 (c) 46 (d) 44
  39. 39.What is the missing term in the AP 7, ?, 17, 22, 27? (a) 12 (b) 13 (c) 11 (d) 17
  40. 40.Which term of the AP 17, 25, 33, 41, … is 273? (a) 34th (b) 35th (c) 32nd (d) 33rd

Answer key

  1. 246
  2. 820
  3. 315
  4. 81
  5. 84
  6. 125
  7. 111
  8. 1431
  9. 29
  10. 50
  11. 11
  12. 1485
  13. 25
  14. 946
  15. 110
  16. 25
  17. 396
  18. 32
  19. 95
  20. 361
  21. 217
  22. 150
  23. 15th
  24. 125
  25. 576
  26. 9
  27. 440
  28. 192
  29. 88
  30. 119
  31. 25
  32. 94
  33. 72
  34. 340
  35. 39
  36. 441
  37. 195
  38. 48
  39. 12
  40. 33rd

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