← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 669 · 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 6 terms of the AP 1, 6, 11, …? (a) 162 (b) 26 (c) 96 (d) 81
  2. 2.What is the 13th term of the AP 12, 16, 20, 24, …? (a) 60 (b) 52 (c) 64 (d) 48
  3. 3.What is the 38th term of the AP 19, 22, 25, 28, …? (a) 130 (b) 133 (c) 111 (d) 114
  4. 4.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 100 (c) 110 (d) 55
  5. 5.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 35 (b) 11 (c) 70 (d) 40
  6. 6.What is the 18th term of the AP 20, 27, 34, 41, …? (a) 126 (b) 119 (c) 139 (d) 146
  7. 7.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 189 (b) 378 (c) 194 (d) 41
  8. 8.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 45 (c) 81 (d) 90
  9. 9.Which term of the AP 17, 25, 33, 41, … is 217? (a) 25th (b) 26th (c) 28th (d) 27th
  10. 10.What is the 26th term of the AP 15, 24, 33, 42, …? (a) 234 (b) 225 (c) 240 (d) 249
  11. 11.What is the missing term in the AP 6, 8, ?, 12, 14? (a) 12 (b) 10 (c) 11 (d) 9
  12. 12.What is the 34th term of the AP 8, 11, 14, 17, …? (a) 107 (b) 102 (c) 110 (d) 99
  13. 13.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 650 (d) 625
  14. 14.What is the sum of the first 9 terms of the AP 8, 14, 20, …? (a) 288 (b) 315 (c) 56 (d) 576
  15. 15.What is the sum of the first 5 terms of the AP 3, 6, 9, …? (a) 48 (b) 45 (c) 15 (d) 90
  16. 16.What is the sum of all the whole numbers from 1 to 64? (a) 4160 (b) 2048 (c) 2016 (d) 2080
  17. 17.Which term of the AP 16, 20, 24, 28, … is 120? (a) 26th (b) 28th (c) 30th (d) 27th
  18. 18.What is the 23rd term of the AP 15, 23, 31, 39, …? (a) 191 (b) 184 (c) 176 (d) 199
  19. 19.What is the 18th term of the AP 19, 22, 25, 28, …? (a) 54 (b) 70 (c) 73 (d) 51
  20. 20.What is the 37th term of the AP 20, 27, 34, 41, …? (a) 279 (b) 252 (c) 259 (d) 272
  21. 21.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 36 (c) 64 (d) 72
  22. 22.What is the 28th term of the AP 5, 13, 21, 29, …? (a) 224 (b) 216 (c) 221 (d) 229
  23. 23.What is the missing term in the AP 17, ?, 35, 44, 53? (a) 27 (b) 26 (c) 35 (d) 25
  24. 24.What is the 11th term of the AP 16, 22, 28, 34, …? (a) 82 (b) 76 (c) 66 (d) 60
  25. 25.What is the 22nd term of the AP 19, 25, 31, 37, …? (a) 132 (b) 145 (c) 126 (d) 151
  26. 26.What is the 16th term of the AP 2, 9, 16, 23, …? (a) 112 (b) 107 (c) 105 (d) 114
  27. 27.Which term of the AP 19, 27, 35, 43, … is 171? (a) 21st (b) 19th (c) 20th (d) 22nd
  28. 28.Which term of the AP 6, 12, 18, 24, … is 84? (a) 16th (b) 13th (c) 15th (d) 14th
  29. 29.What is the missing term in the AP 13, 21, 29, ?, 45? (a) 36 (b) 38 (c) 37 (d) 45
  30. 30.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 126 (b) 64 (c) 63 (d) 11
  31. 31.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 160 (b) 26 (c) 85 (d) 80
  32. 32.What is the missing term in the AP 18, 20, ?, 24, 26? (a) 21 (b) 22 (c) 23 (d) 24
  33. 33.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 992 (c) 497 (d) 496
  34. 34.Which term of the AP 2, 5, 8, 11, … is 80? (a) 26th (b) 29th (c) 27th (d) 28th
  35. 35.Which term of the AP 14, 17, 20, 23, … is 92? (a) 29th (b) 28th (c) 27th (d) 26th
  36. 36.What is the sum of all the whole numbers from 1 to 22? (a) 242 (b) 506 (c) 231 (d) 253
  37. 37.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 78 (b) 77 (c) 154 (d) 12
  38. 38.What is the 34th term of the AP 5, 12, 19, 26, …? (a) 243 (b) 236 (c) 231 (d) 238
  39. 39.What is the sum of the first 10 terms of the AP 5, 9, 13, …? (a) 41 (b) 230 (c) 460 (d) 250
  40. 40.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 784 (c) 406 (d) 812

Answer key

  1. 81
  2. 60
  3. 130
  4. 100
  5. 35
  6. 139
  7. 189
  8. 81
  9. 26th
  10. 240
  11. 10
  12. 107
  13. 625
  14. 288
  15. 45
  16. 2080
  17. 27th
  18. 191
  19. 70
  20. 272
  21. 64
  22. 221
  23. 26
  24. 76
  25. 145
  26. 107
  27. 20th
  28. 14th
  29. 37
  30. 63
  31. 80
  32. 22
  33. 496
  34. 27th
  35. 27th
  36. 253
  37. 77
  38. 236
  39. 230
  40. 784

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