← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 194 · 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 all the whole numbers from 1 to 35? (a) 1260 (b) 630 (c) 595 (d) 631
  2. 2.What is the sum of the first 7 terms of the AP 3, 6, 9, …? (a) 87 (b) 168 (c) 84 (d) 21
  3. 3.What is the 35th term of the AP 15, 22, 29, 36, …? (a) 245 (b) 260 (c) 253 (d) 238
  4. 4.Which term of the AP 16, 24, 32, 40, … is 272? (a) 33rd (b) 34th (c) 32nd (d) 35th
  5. 5.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 17 (c) 81 (d) 45
  6. 6.What is the 40th term of the AP 4, 9, 14, 19, …? (a) 200 (b) 195 (c) 199 (d) 204
  7. 7.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 260 (b) 46 (c) 470 (d) 235
  8. 8.What is the sum of the first 9 terms of the AP 10, 14, 18, …? (a) 42 (b) 252 (c) 468 (d) 234
  9. 9.What is the 30th term of the AP 11, 13, 15, 17, …? (a) 60 (b) 71 (c) 58 (d) 69
  10. 10.What is the 10th term of the AP 5, 8, 11, 14, …? (a) 30 (b) 27 (c) 32 (d) 35
  11. 11.What is the 29th term of the AP 16, 19, 22, 25, …? (a) 87 (b) 84 (c) 100 (d) 103
  12. 12.Which term of the AP 4, 13, 22, 31, … is 112? (a) 15th (b) 12th (c) 14th (d) 13th
  13. 13.What is the sum of all the whole numbers from 1 to 23? (a) 277 (b) 552 (c) 276 (d) 253
  14. 14.What is the 25th term of the AP 20, 27, 34, 41, …? (a) 195 (b) 175 (c) 188 (d) 168
  15. 15.What is the 16th term of the AP 2, 11, 20, 29, …? (a) 144 (b) 135 (c) 146 (d) 137
  16. 16.What is the sum of the first 8 terms of the AP 2, 5, 8, …? (a) 200 (b) 112 (c) 23 (d) 100
  17. 17.Which term of the AP 1, 4, 7, 10, … is 67? (a) 22nd (b) 24th (c) 23rd (d) 25th
  18. 18.What is the 16th term of the AP 8, 15, 22, 29, …? (a) 105 (b) 112 (c) 120 (d) 113
  19. 19.What is the sum of all the whole numbers from 1 to 39? (a) 780 (b) 1560 (c) 741 (d) 781
  20. 20.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 138 (b) 240 (c) 35 (d) 120
  21. 21.Which term of the AP 3, 12, 21, 30, … is 300? (a) 34th (b) 33rd (c) 36th (d) 35th
  22. 22.What is the 25th term of the AP 2, 4, 6, 8, …? (a) 48 (b) 51 (c) 52 (d) 50
  23. 23.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 52 (b) 302 (c) 594 (d) 297
  24. 24.What is the 30th term of the AP 1, 6, 11, 16, …? (a) 145 (b) 146 (c) 150 (d) 151
  25. 25.What is the missing term in the AP 10, 12, ?, 16, 18? (a) 15 (b) 16 (c) 14 (d) 13
  26. 26.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 21 (c) 132 (d) 121
  27. 27.Which term of the AP 8, 15, 22, 29, … is 190? (a) 26th (b) 28th (c) 27th (d) 29th
  28. 28.Which term of the AP 4, 12, 20, 28, … is 196? (a) 25th (b) 26th (c) 24th (d) 27th
  29. 29.What is the sum of all the whole numbers from 1 to 16? (a) 120 (b) 128 (c) 136 (d) 272
  30. 30.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 100 (b) 51 (c) 50 (d) 12
  31. 31.What is the sum of all the whole numbers from 1 to 92? (a) 4186 (b) 8556 (c) 4232 (d) 4278
  32. 32.What is the 33rd term of the AP 15, 18, 21, 24, …? (a) 111 (b) 99 (c) 96 (d) 114
  33. 33.What is the sum of the first 10 terms of the AP 4, 5, 6, …? (a) 170 (b) 90 (c) 85 (d) 13
  34. 34.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 25 (d) 15
  35. 35.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 60 (b) 120 (c) 11 (d) 64
  36. 36.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 264 (b) 150 (c) 37 (d) 132
  37. 37.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 190 (b) 28 (c) 200 (d) 380
  38. 38.What is the 19th term of the AP 11, 14, 17, 20, …? (a) 68 (b) 57 (c) 65 (d) 54
  39. 39.What is the missing term in the AP 7, 16, 25, ?, 43? (a) 34 (b) 33 (c) 35 (d) 43
  40. 40.What is the 19th term of the AP 8, 14, 20, 26, …? (a) 108 (b) 122 (c) 114 (d) 116

Answer key

  1. 630
  2. 84
  3. 253
  4. 33rd
  5. 81
  6. 199
  7. 235
  8. 234
  9. 69
  10. 32
  11. 100
  12. 13th
  13. 276
  14. 188
  15. 137
  16. 100
  17. 23rd
  18. 113
  19. 780
  20. 120
  21. 34th
  22. 50
  23. 297
  24. 146
  25. 14
  26. 121
  27. 27th
  28. 25th
  29. 136
  30. 50
  31. 4278
  32. 111
  33. 85
  34. 25
  35. 60
  36. 132
  37. 190
  38. 65
  39. 34
  40. 116

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