← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 483 · 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 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 325 (c) 650 (d) 625
  2. 2.What is the 33rd term of the AP 7, 11, 15, 19, …? (a) 128 (b) 132 (c) 139 (d) 135
  3. 3.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 186 (b) 21 (c) 192 (d) 372
  4. 4.Which term of the AP 16, 20, 24, 28, … is 160? (a) 38th (b) 40th (c) 36th (d) 37th
  5. 5.What is the 17th term of the AP 6, 13, 20, 27, …? (a) 125 (b) 118 (c) 112 (d) 119
  6. 6.What is the sum of the first 10 terms of the AP 7, 10, 13, …? (a) 34 (b) 410 (c) 220 (d) 205
  7. 7.What is the 37th term of the AP 13, 22, 31, 40, …? (a) 324 (b) 333 (c) 346 (d) 337
  8. 8.What is the missing term in the AP 14, 22, ?, 38, 46? (a) 31 (b) 38 (c) 29 (d) 30
  9. 9.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 11 (b) 126 (c) 63 (d) 64
  10. 10.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 13 (b) 48 (c) 96 (d) 54
  11. 11.What is the 13th term of the AP 10, 17, 24, 31, …? (a) 84 (b) 101 (c) 91 (d) 94
  12. 12.What is the sum of the first 9 terms of the AP 8, 12, 16, …? (a) 216 (b) 432 (c) 234 (d) 40
  13. 13.What is the 38th term of the AP 7, 14, 21, 28, …? (a) 273 (b) 259 (c) 267 (d) 266
  14. 14.What is the sum of the first 7 terms of the AP 6, 12, 18, …? (a) 189 (b) 168 (c) 336 (d) 42
  15. 15.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 144 (b) 18 (c) 143 (d) 286
  16. 16.What is the 38th term of the AP 18, 21, 24, 27, …? (a) 129 (b) 111 (c) 132 (d) 114
  17. 17.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 25 (d) 9
  18. 18.What is the sum of all the whole numbers from 1 to 88? (a) 3828 (b) 3872 (c) 7832 (d) 3916
  19. 19.What is the missing term in the AP 17, 23, 29, ?, 41? (a) 34 (b) 36 (c) 35 (d) 41
  20. 20.What is the 28th term of the AP 12, 19, 26, 33, …? (a) 189 (b) 201 (c) 208 (d) 196
  21. 21.What is the 40th term of the AP 4, 6, 8, 10, …? (a) 78 (b) 80 (c) 82 (d) 84
  22. 22.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 78 (c) 144 (d) 23
  23. 23.What is the sum of the first 12 terms of the AP 3, 5, 7, …? (a) 336 (b) 25 (c) 168 (d) 180
  24. 24.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 272 (c) 256 (d) 31
  25. 25.What is the sum of all the whole numbers from 1 to 30? (a) 450 (b) 930 (c) 465 (d) 435
  26. 26.What is the 38th term of the AP 13, 19, 25, 31, …? (a) 222 (b) 241 (c) 228 (d) 235
  27. 27.What is the sum of all the whole numbers from 1 to 71? (a) 2485 (b) 5112 (c) 2556 (d) 2557
  28. 28.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 351 (c) 51 (d) 676
  29. 29.What is the sum of all the whole numbers from 1 to 49? (a) 1225 (b) 2450 (c) 1176 (d) 1226
  30. 30.What is the 29th term of the AP 15, 18, 21, 24, …? (a) 102 (b) 99 (c) 87 (d) 84
  31. 31.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 105 (c) 196 (d) 210
  32. 32.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 171 (b) 306 (c) 153 (d) 33
  33. 33.What is the 23rd term of the AP 2, 4, 6, 8, …? (a) 48 (b) 44 (c) 47 (d) 46
  34. 34.What is the 14th term of the AP 13, 15, 17, 19, …? (a) 28 (b) 26 (c) 41 (d) 39
  35. 35.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 552 (c) 529 (d) 276
  36. 36.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 210 (b) 114 (c) 105 (d) 25
  37. 37.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 2145 (c) 2211 (d) 4422
  38. 38.What is the 30th term of the AP 6, 10, 14, 18, …? (a) 116 (b) 126 (c) 120 (d) 122
  39. 39.What is the sum of all the whole numbers from 1 to 96? (a) 9312 (b) 4656 (c) 4608 (d) 4560
  40. 40.What is the sum of the first 11 terms of the AP 1, 5, 9, …? (a) 253 (b) 41 (c) 231 (d) 462

Answer key

  1. 625
  2. 135
  3. 186
  4. 37th
  5. 118
  6. 205
  7. 337
  8. 30
  9. 63
  10. 48
  11. 94
  12. 216
  13. 266
  14. 168
  15. 143
  16. 129
  17. 25
  18. 3916
  19. 35
  20. 201
  21. 82
  22. 144
  23. 168
  24. 256
  25. 465
  26. 235
  27. 2556
  28. 676
  29. 1225
  30. 99
  31. 196
  32. 153
  33. 46
  34. 39
  35. 529
  36. 105
  37. 2211
  38. 122
  39. 4656
  40. 231

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