← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 413 · 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 46? (a) 1081 (b) 1035 (c) 1058 (d) 2162
  2. 2.What is the 16th term of the AP 18, 20, 22, 24, …? (a) 32 (b) 30 (c) 48 (d) 50
  3. 3.What is the 32nd term of the AP 20, 22, 24, 26, …? (a) 84 (b) 64 (c) 62 (d) 82
  4. 4.What is the 10th term of the AP 17, 23, 29, 35, …? (a) 60 (b) 77 (c) 71 (d) 54
  5. 5.What is the sum of the first 12 terms of the AP 8, 9, 10, …? (a) 19 (b) 324 (c) 162 (d) 168
  6. 6.What is the missing term in the AP 5, 7, 9, ?, 13? (a) 10 (b) 12 (c) 11 (d) 13
  7. 7.What is the sum of the first 11 terms of the AP 10, 13, 16, …? (a) 40 (b) 550 (c) 275 (d) 278
  8. 8.What is the missing term in the AP 9, 14, 19, ?, 29? (a) 25 (b) 29 (c) 24 (d) 23
  9. 9.What is the 23rd term of the AP 12, 19, 26, 33, …? (a) 161 (b) 154 (c) 173 (d) 166
  10. 10.What is the missing term in the AP 2, 9, ?, 23, 30? (a) 15 (b) 17 (c) 16 (d) 23
  11. 11.What is the 13th term of the AP 7, 11, 15, 19, …? (a) 55 (b) 52 (c) 48 (d) 59
  12. 12.What is the 28th term of the AP 9, 17, 25, 33, …? (a) 224 (b) 233 (c) 225 (d) 216
  13. 13.What is the sum of the first 6 terms of the AP 6, 8, 10, …? (a) 132 (b) 72 (c) 16 (d) 66
  14. 14.Which term of the AP 20, 22, 24, 26, … is 72? (a) 27th (b) 36th (c) 28th (d) 26th
  15. 15.Which term of the AP 11, 20, 29, 38, … is 236? (a) 27th (b) 28th (c) 26th (d) 25th
  16. 16.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 47 (c) 576 (d) 300
  17. 17.What is the 14th term of the AP 10, 19, 28, 37, …? (a) 126 (b) 127 (c) 136 (d) 117
  18. 18.What is the 25th term of the AP 12, 14, 16, 18, …? (a) 50 (b) 48 (c) 60 (d) 62
  19. 19.What is the 16th term of the AP 15, 19, 23, 27, …? (a) 64 (b) 79 (c) 75 (d) 60
  20. 20.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 42 (b) 12 (c) 84 (d) 48
  21. 21.What is the sum of the first 12 terms of the AP 6, 9, 12, …? (a) 540 (b) 39 (c) 288 (d) 270
  22. 22.What is the missing term in the AP 11, ?, 23, 29, 35? (a) 23 (b) 18 (c) 16 (d) 17
  23. 23.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 210 (c) 400 (d) 420
  24. 24.What is the 27th term of the AP 13, 21, 29, 37, …? (a) 208 (b) 216 (c) 221 (d) 229
  25. 25.What is the sum of all the whole numbers from 1 to 48? (a) 2352 (b) 1176 (c) 1152 (d) 1128
  26. 26.What is the sum of all the whole numbers from 1 to 13? (a) 78 (b) 91 (c) 92 (d) 182
  27. 27.What is the 32nd term of the AP 16, 25, 34, 43, …? (a) 279 (b) 288 (c) 304 (d) 295
  28. 28.What is the sum of the first 10 terms of the AP 9, 12, 15, …? (a) 225 (b) 450 (c) 240 (d) 36
  29. 29.What is the sum of the first 10 terms of the AP 10, 16, 22, …? (a) 400 (b) 740 (c) 64 (d) 370
  30. 30.What is the 15th term of the AP 11, 18, 25, 32, …? (a) 105 (b) 98 (c) 116 (d) 109
  31. 31.Which term of the AP 10, 18, 26, 34, … is 114? (a) 16th (b) 14th (c) 13th (d) 15th
  32. 32.What is the 37th term of the AP 14, 21, 28, 35, …? (a) 259 (b) 266 (c) 273 (d) 252
  33. 33.What is the 32nd term of the AP 5, 10, 15, 20, …? (a) 155 (b) 161 (c) 160 (d) 165
  34. 34.What is the 38th term of the AP 5, 9, 13, 17, …? (a) 157 (b) 152 (c) 148 (d) 153
  35. 35.What is the sum of all the whole numbers from 1 to 60? (a) 3660 (b) 1800 (c) 1830 (d) 1770
  36. 36.What is the sum of the first 10 terms of the AP 7, 10, 13, …? (a) 220 (b) 205 (c) 34 (d) 410
  37. 37.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 15 (c) 25 (d) 9
  38. 38.What is the 16th term of the AP 14, 17, 20, 23, …? (a) 45 (b) 48 (c) 62 (d) 59
  39. 39.Which term of the AP 17, 25, 33, 41, … is 217? (a) 25th (b) 26th (c) 27th (d) 28th
  40. 40.What is the sum of all the whole numbers from 1 to 29? (a) 436 (b) 406 (c) 870 (d) 435

Answer key

  1. 1081
  2. 48
  3. 82
  4. 71
  5. 162
  6. 11
  7. 275
  8. 24
  9. 166
  10. 16
  11. 55
  12. 225
  13. 66
  14. 27th
  15. 26th
  16. 576
  17. 127
  18. 60
  19. 75
  20. 42
  21. 270
  22. 17
  23. 400
  24. 221
  25. 1176
  26. 91
  27. 295
  28. 225
  29. 370
  30. 109
  31. 14th
  32. 266
  33. 160
  34. 153
  35. 1830
  36. 205
  37. 25
  38. 59
  39. 26th
  40. 435

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