← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 190 · 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.Which term of the AP 11, 17, 23, 29, … is 215? (a) 37th (b) 36th (c) 34th (d) 35th
  2. 2.What is the 33rd term of the AP 3, 10, 17, 24, …? (a) 231 (b) 234 (c) 227 (d) 224
  3. 3.What is the 34th term of the AP 20, 24, 28, 32, …? (a) 132 (b) 152 (c) 136 (d) 156
  4. 4.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 56 (b) 28 (c) 7 (d) 29
  5. 5.What is the 39th term of the AP 18, 20, 22, 24, …? (a) 94 (b) 78 (c) 96 (d) 76
  6. 6.What is the missing term in the AP 4, 6, 8, ?, 12? (a) 11 (b) 9 (c) 12 (d) 10
  7. 7.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 324 (b) 171 (c) 26 (d) 162
  8. 8.What is the sum of all the whole numbers from 1 to 25? (a) 325 (b) 326 (c) 300 (d) 650
  9. 9.What is the 39th term of the AP 5, 12, 19, 26, …? (a) 278 (b) 273 (c) 266 (d) 271
  10. 10.What is the sum of all the whole numbers from 1 to 45? (a) 2070 (b) 1035 (c) 1036 (d) 990
  11. 11.What is the 12th term of the AP 5, 7, 9, 11, …? (a) 27 (b) 29 (c) 24 (d) 22
  12. 12.What is the missing term in the AP 20, ?, 24, 26, 28? (a) 24 (b) 23 (c) 21 (d) 22
  13. 13.What is the 18th term of the AP 6, 15, 24, 33, …? (a) 159 (b) 153 (c) 168 (d) 162
  14. 14.What is the 30th term of the AP 11, 16, 21, 26, …? (a) 150 (b) 145 (c) 161 (d) 156
  15. 15.Which term of the AP 20, 26, 32, 38, … is 104? (a) 17th (b) 15th (c) 16th (d) 14th
  16. 16.What is the sum of the first 5 terms of the AP 5, 6, 7, …? (a) 70 (b) 35 (c) 9 (d) 36
  17. 17.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 43 (c) 484 (d) 253
  18. 18.Which term of the AP 3, 9, 15, 21, … is 201? (a) 35th (b) 33rd (c) 34th (d) 36th
  19. 19.What is the 19th term of the AP 2, 9, 16, 23, …? (a) 135 (b) 133 (c) 128 (d) 126
  20. 20.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 31 (c) 256 (d) 272
  21. 21.What is the sum of all the whole numbers from 1 to 19? (a) 380 (b) 171 (c) 190 (d) 191
  22. 22.Which term of the AP 5, 14, 23, 32, … is 167? (a) 20th (b) 19th (c) 18th (d) 21st
  23. 23.What is the 13th term of the AP 12, 19, 26, 33, …? (a) 91 (b) 84 (c) 96 (d) 103
  24. 24.What is the 36th term of the AP 6, 8, 10, 12, …? (a) 78 (b) 70 (c) 72 (d) 76
  25. 25.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 162 (b) 180 (c) 324 (d) 34
  26. 26.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 136 (b) 29 (c) 120 (d) 240
  27. 27.What is the sum of all the whole numbers from 1 to 91? (a) 4187 (b) 4186 (c) 4095 (d) 8372
  28. 28.What is the 26th term of the AP 18, 26, 34, 42, …? (a) 208 (b) 226 (c) 218 (d) 200
  29. 29.What is the sum of the first 8 terms of the AP 8, 10, 12, …? (a) 240 (b) 22 (c) 128 (d) 120
  30. 30.What is the missing term in the AP 19, 22, 25, ?, 31? (a) 27 (b) 31 (c) 28 (d) 29
  31. 31.What is the sum of the first 12 terms of the AP 6, 8, 10, …? (a) 408 (b) 216 (c) 204 (d) 28
  32. 32.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 84 (b) 19 (c) 90 (d) 168
  33. 33.What is the missing term in the AP 10, 13, ?, 19, 22? (a) 15 (b) 16 (c) 19 (d) 17
  34. 34.What is the 37th term of the AP 6, 13, 20, 27, …? (a) 252 (b) 258 (c) 259 (d) 265
  35. 35.Which term of the AP 6, 10, 14, 18, … is 90? (a) 24th (b) 23rd (c) 22nd (d) 21st
  36. 36.What is the sum of all the whole numbers from 1 to 64? (a) 4160 (b) 2016 (c) 2048 (d) 2080
  37. 37.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 30 (b) 144 (c) 128 (d) 256
  38. 38.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 49 (c) 28 (d) 56
  39. 39.What is the missing term in the AP 2, 8, 14, ?, 26? (a) 21 (b) 19 (c) 26 (d) 20
  40. 40.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 132 (c) 21 (d) 66

Answer key

  1. 35th
  2. 227
  3. 152
  4. 28
  5. 94
  6. 10
  7. 162
  8. 325
  9. 271
  10. 1035
  11. 27
  12. 22
  13. 159
  14. 156
  15. 15th
  16. 35
  17. 484
  18. 34th
  19. 128
  20. 256
  21. 190
  22. 19th
  23. 96
  24. 76
  25. 162
  26. 120
  27. 4186
  28. 218
  29. 120
  30. 28
  31. 204
  32. 84
  33. 16
  34. 258
  35. 22nd
  36. 2080
  37. 128
  38. 49
  39. 20
  40. 121

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