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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 722 · 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 17th term of the AP 10, 15, 20, 25, …? (a) 95 (b) 85 (c) 80 (d) 90
  2. 2.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 30 (b) 50 (c) 25 (d) 9
  3. 3.What is the 38th term of the AP 6, 13, 20, 27, …? (a) 266 (b) 265 (c) 259 (d) 272
  4. 4.What is the sum of all the whole numbers from 1 to 19? (a) 190 (b) 380 (c) 171 (d) 191
  5. 5.What is the 26th term of the AP 18, 25, 32, 39, …? (a) 200 (b) 182 (c) 175 (d) 193
  6. 6.What is the 39th term of the AP 10, 16, 22, 28, …? (a) 234 (b) 238 (c) 228 (d) 244
  7. 7.What is the missing term in the AP 20, 23, ?, 29, 32? (a) 26 (b) 27 (c) 25 (d) 29
  8. 8.What is the missing term in the AP 5, 14, 23, ?, 41? (a) 32 (b) 31 (c) 41 (d) 33
  9. 9.What is the 26th term of the AP 1, 3, 5, 7, …? (a) 52 (b) 53 (c) 51 (d) 50
  10. 10.What is the missing term in the AP 2, ?, 8, 11, 14? (a) 6 (b) 4 (c) 5 (d) 8
  11. 11.What is the 23rd term of the AP 16, 24, 32, 40, …? (a) 184 (b) 176 (c) 192 (d) 200
  12. 12.What is the sum of all the whole numbers from 1 to 34? (a) 595 (b) 1190 (c) 578 (d) 561
  13. 13.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 182 (c) 25 (d) 169
  14. 14.What is the missing term in the AP 12, 20, ?, 36, 44? (a) 36 (b) 28 (c) 29 (d) 27
  15. 15.Which term of the AP 2, 7, 12, 17, … is 157? (a) 32nd (b) 34th (c) 33rd (d) 31st
  16. 16.What is the 25th term of the AP 2, 7, 12, 17, …? (a) 120 (b) 125 (c) 127 (d) 122
  17. 17.What is the 35th term of the AP 6, 9, 12, 15, …? (a) 111 (b) 102 (c) 108 (d) 105
  18. 18.Which term of the AP 9, 15, 21, 27, … is 165? (a) 26th (b) 29th (c) 27th (d) 28th
  19. 19.What is the sum of all the whole numbers from 1 to 96? (a) 4560 (b) 4608 (c) 9312 (d) 4656
  20. 20.What is the sum of all the whole numbers from 1 to 67? (a) 2278 (b) 4556 (c) 2211 (d) 2279
  21. 21.What is the 29th term of the AP 14, 20, 26, 32, …? (a) 182 (b) 168 (c) 188 (d) 174
  22. 22.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 53 (b) 50 (c) 16 (d) 100
  23. 23.What is the missing term in the AP 15, 21, 27, ?, 39? (a) 34 (b) 33 (c) 39 (d) 32
  24. 24.What is the 32nd term of the AP 17, 25, 33, 41, …? (a) 273 (b) 265 (c) 256 (d) 248
  25. 25.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 64 (c) 36 (d) 15
  26. 26.What is the 35th term of the AP 2, 6, 10, 14, …? (a) 140 (b) 138 (c) 142 (d) 136
  27. 27.What is the 14th term of the AP 1, 4, 7, 10, …? (a) 40 (b) 43 (c) 42 (d) 39
  28. 28.What is the sum of the first 5 terms of the AP 6, 12, 18, …? (a) 105 (b) 180 (c) 90 (d) 30
  29. 29.Which term of the AP 4, 10, 16, 22, … is 196? (a) 34th (b) 35th (c) 32nd (d) 33rd
  30. 30.What is the sum of all the whole numbers from 1 to 23? (a) 552 (b) 277 (c) 253 (d) 276
  31. 31.What is the missing term in the AP 8, ?, 14, 17, 20? (a) 10 (b) 11 (c) 14 (d) 12
  32. 32.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 15 (b) 78 (c) 75 (d) 150
  33. 33.What is the 20th term of the AP 5, 7, 9, 11, …? (a) 43 (b) 38 (c) 45 (d) 40
  34. 34.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 2145 (c) 2211 (d) 4422
  35. 35.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 21 (c) 11 (d) 42
  36. 36.What is the 18th term of the AP 18, 20, 22, 24, …? (a) 36 (b) 52 (c) 34 (d) 54
  37. 37.What is the 40th term of the AP 5, 11, 17, 23, …? (a) 234 (b) 240 (c) 239 (d) 245
  38. 38.What is the sum of the first 8 terms of the AP 3, 8, 13, …? (a) 328 (b) 184 (c) 38 (d) 164
  39. 39.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 55 (b) 10 (c) 54 (d) 108
  40. 40.What is the 13th term of the AP 8, 13, 18, 23, …? (a) 60 (b) 65 (c) 73 (d) 68

Answer key

  1. 90
  2. 25
  3. 265
  4. 190
  5. 193
  6. 238
  7. 26
  8. 32
  9. 51
  10. 5
  11. 192
  12. 595
  13. 169
  14. 28
  15. 32nd
  16. 122
  17. 108
  18. 27th
  19. 4656
  20. 2278
  21. 182
  22. 50
  23. 33
  24. 265
  25. 64
  26. 138
  27. 40
  28. 90
  29. 33rd
  30. 276
  31. 11
  32. 75
  33. 43
  34. 2211
  35. 36
  36. 52
  37. 239
  38. 164
  39. 54
  40. 68

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