← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 317 · 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 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 81 (c) 45 (d) 17
  2. 2.What is the 29th term of the AP 4, 13, 22, 31, …? (a) 265 (b) 256 (c) 261 (d) 252
  3. 3.What is the missing term in the AP 5, ?, 17, 23, 29? (a) 11 (b) 12 (c) 17 (d) 10
  4. 4.What is the 10th term of the AP 17, 24, 31, 38, …? (a) 63 (b) 87 (c) 70 (d) 80
  5. 5.What is the missing term in the AP 16, ?, 32, 40, 48? (a) 23 (b) 24 (c) 25 (d) 32
  6. 6.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 169 (c) 91 (d) 182
  7. 7.Which term of the AP 19, 21, 23, 25, … is 69? (a) 25th (b) 28th (c) 26th (d) 27th
  8. 8.What is the 40th term of the AP 20, 26, 32, 38, …? (a) 234 (b) 254 (c) 240 (d) 260
  9. 9.What is the sum of all the whole numbers from 1 to 13? (a) 92 (b) 78 (c) 182 (d) 91
  10. 10.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 37 (b) 150 (c) 132 (d) 264
  11. 11.What is the missing term in the AP 6, 10, ?, 18, 22? (a) 13 (b) 14 (c) 15 (d) 18
  12. 12.What is the 28th term of the AP 7, 15, 23, 31, …? (a) 223 (b) 231 (c) 216 (d) 224
  13. 13.What is the sum of the first 11 terms of the AP 5, 11, 17, …? (a) 385 (b) 65 (c) 418 (d) 770
  14. 14.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 55 (c) 110 (d) 19
  15. 15.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 408 (b) 67 (c) 444 (d) 816
  16. 16.What is the 15th term of the AP 1, 5, 9, 13, …? (a) 61 (b) 57 (c) 56 (d) 60
  17. 17.What is the sum of the first 8 terms of the AP 9, 15, 21, …? (a) 480 (b) 264 (c) 240 (d) 51
  18. 18.What is the sum of the first 7 terms of the AP 6, 12, 18, …? (a) 168 (b) 189 (c) 336 (d) 42
  19. 19.What is the sum of all the whole numbers from 1 to 10? (a) 110 (b) 45 (c) 55 (d) 50
  20. 20.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 21 (c) 42 (d) 36
  21. 21.What is the 27th term of the AP 13, 16, 19, 22, …? (a) 94 (b) 78 (c) 81 (d) 91
  22. 22.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 59 (c) 930 (d) 900
  23. 23.Which term of the AP 4, 9, 14, 19, … is 44? (a) 11th (b) 8th (c) 10th (d) 9th
  24. 24.What is the 25th term of the AP 19, 26, 33, 40, …? (a) 194 (b) 187 (c) 168 (d) 175
  25. 25.What is the sum of the first 11 terms of the AP 10, 13, 16, …? (a) 275 (b) 550 (c) 40 (d) 278
  26. 26.What is the 40th term of the AP 13, 20, 27, 34, …? (a) 273 (b) 293 (c) 280 (d) 286
  27. 27.What is the 38th term of the AP 15, 19, 23, 27, …? (a) 167 (b) 152 (c) 163 (d) 148
  28. 28.What is the 32nd term of the AP 18, 20, 22, 24, …? (a) 82 (b) 62 (c) 64 (d) 80
  29. 29.What is the sum of the first 8 terms of the AP 8, 11, 14, …? (a) 296 (b) 160 (c) 29 (d) 148
  30. 30.What is the 39th term of the AP 5, 9, 13, 17, …? (a) 157 (b) 161 (c) 156 (d) 152
  31. 31.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 176 (b) 96 (c) 88 (d) 18
  32. 32.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 220 (b) 110 (c) 120 (d) 20
  33. 33.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 130 (b) 11 (c) 65 (d) 70
  34. 34.What is the sum of the first 12 terms of the AP 4, 7, 10, …? (a) 492 (b) 264 (c) 246 (d) 37
  35. 35.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 66 (c) 132 (d) 121
  36. 36.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 15 (c) 9 (d) 30
  37. 37.Which term of the AP 11, 19, 27, 35, … is 115? (a) 14th (b) 16th (c) 15th (d) 13th
  38. 38.What is the missing term in the AP 16, ?, 20, 22, 24? (a) 17 (b) 18 (c) 20 (d) 19
  39. 39.What is the sum of the first 12 terms of the AP 8, 9, 10, …? (a) 168 (b) 324 (c) 162 (d) 19
  40. 40.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 435 (c) 436 (d) 406

Answer key

  1. 81
  2. 256
  3. 11
  4. 80
  5. 24
  6. 169
  7. 26th
  8. 254
  9. 91
  10. 132
  11. 14
  12. 223
  13. 385
  14. 100
  15. 408
  16. 57
  17. 240
  18. 168
  19. 55
  20. 36
  21. 91
  22. 900
  23. 9th
  24. 187
  25. 275
  26. 286
  27. 163
  28. 80
  29. 148
  30. 157
  31. 88
  32. 110
  33. 65
  34. 246
  35. 121
  36. 25
  37. 14th
  38. 18
  39. 162
  40. 435

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