← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 501 · 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 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 13 (c) 56 (d) 28
  2. 2.Which term of the AP 8, 11, 14, 17, … is 98? (a) 32nd (b) 30th (c) 31st (d) 33rd
  3. 3.What is the sum of all the whole numbers from 1 to 20? (a) 190 (b) 200 (c) 420 (d) 210
  4. 4.What is the sum of the first 9 terms of the AP 7, 9, 11, …? (a) 23 (b) 270 (c) 144 (d) 135
  5. 5.What is the missing term in the AP 5, ?, 9, 11, 13? (a) 6 (b) 8 (c) 7 (d) 9
  6. 6.Which term of the AP 20, 26, 32, 38, … is 104? (a) 16th (b) 17th (c) 15th (d) 14th
  7. 7.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 45 (c) 90 (d) 81
  8. 8.What is the sum of all the whole numbers from 1 to 29? (a) 436 (b) 406 (c) 870 (d) 435
  9. 9.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 55 (c) 784 (d) 812
  10. 10.Which term of the AP 16, 24, 32, 40, … is 296? (a) 35th (b) 37th (c) 38th (d) 36th
  11. 11.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 15 (d) 25
  12. 12.What is the 27th term of the AP 9, 17, 25, 33, …? (a) 208 (b) 217 (c) 216 (d) 225
  13. 13.What is the 35th term of the AP 17, 20, 23, 26, …? (a) 105 (b) 122 (c) 119 (d) 102
  14. 14.What is the 17th term of the AP 19, 27, 35, 43, …? (a) 136 (b) 147 (c) 128 (d) 155
  15. 15.What is the 24th term of the AP 19, 24, 29, 34, …? (a) 115 (b) 134 (c) 120 (d) 139
  16. 16.What is the sum of all the whole numbers from 1 to 43? (a) 903 (b) 1892 (c) 947 (d) 946
  17. 17.What is the 18th term of the AP 5, 10, 15, 20, …? (a) 85 (b) 90 (c) 95 (d) 91
  18. 18.What is the sum of the first 7 terms of the AP 3, 8, 13, …? (a) 252 (b) 131 (c) 126 (d) 33
  19. 19.What is the sum of the first 7 terms of the AP 6, 11, 16, …? (a) 36 (b) 147 (c) 294 (d) 152
  20. 20.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 80 (b) 16 (c) 72 (d) 144
  21. 21.Which term of the AP 4, 6, 8, 10, … is 48? (a) 25th (b) 24th (c) 23rd (d) 22nd
  22. 22.What is the missing term in the AP 3, 5, 7, ?, 11? (a) 10 (b) 11 (c) 9 (d) 8
  23. 23.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 53 (c) 378 (d) 756
  24. 24.What is the missing term in the AP 4, 6, 8, ?, 12? (a) 10 (b) 12 (c) 9 (d) 11
  25. 25.What is the sum of the first 9 terms of the AP 1, 2, 3, …? (a) 45 (b) 9 (c) 90 (d) 46
  26. 26.What is the sum of the first 7 terms of the AP 2, 8, 14, …? (a) 280 (b) 140 (c) 161 (d) 38
  27. 27.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 150 (b) 78 (c) 75 (d) 15
  28. 28.What is the sum of all the whole numbers from 1 to 53? (a) 2862 (b) 1432 (c) 1431 (d) 1378
  29. 29.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 42 (b) 6 (c) 24 (d) 21
  30. 30.Which term of the AP 8, 11, 14, 17, … is 38? (a) 13th (b) 11th (c) 12th (d) 10th
  31. 31.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 29 (b) 114 (c) 99 (d) 198
  32. 32.What is the 16th term of the AP 16, 25, 34, 43, …? (a) 135 (b) 144 (c) 160 (d) 151
  33. 33.Which term of the AP 16, 22, 28, 34, … is 70? (a) 9th (b) 11th (c) 10th (d) 12th
  34. 34.What is the sum of the first 8 terms of the AP 1, 6, 11, …? (a) 296 (b) 36 (c) 168 (d) 148
  35. 35.What is the sum of the first 9 terms of the AP 5, 10, 15, …? (a) 225 (b) 45 (c) 230 (d) 450
  36. 36.Which term of the AP 1, 4, 7, 10, … is 118? (a) 41st (b) 40th (c) 39th (d) 42nd
  37. 37.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 65 (b) 25 (c) 80 (d) 130
  38. 38.What is the missing term in the AP 19, ?, 31, 37, 43? (a) 31 (b) 26 (c) 24 (d) 25
  39. 39.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 72 (c) 36 (d) 64
  40. 40.Which term of the AP 5, 11, 17, 23, … is 101? (a) 18th (b) 19th (c) 17th (d) 16th

Answer key

  1. 49
  2. 31st
  3. 210
  4. 135
  5. 7
  6. 15th
  7. 81
  8. 435
  9. 784
  10. 36th
  11. 25
  12. 217
  13. 119
  14. 147
  15. 134
  16. 946
  17. 90
  18. 126
  19. 147
  20. 72
  21. 23rd
  22. 9
  23. 729
  24. 10
  25. 45
  26. 140
  27. 75
  28. 1431
  29. 21
  30. 11th
  31. 99
  32. 151
  33. 10th
  34. 148
  35. 225
  36. 40th
  37. 65
  38. 25
  39. 64
  40. 17th

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