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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 102 · 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 2, 7, 12, 17, … is 132? (a) 28th (b) 29th (c) 27th (d) 26th
  2. 2.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 210 (b) 420 (c) 230 (d) 39
  3. 3.What is the 30th term of the AP 2, 10, 18, 26, …? (a) 232 (b) 242 (c) 234 (d) 240
  4. 4.What is the 17th term of the AP 12, 17, 22, 27, …? (a) 97 (b) 80 (c) 92 (d) 85
  5. 5.What is the 10th term of the AP 7, 14, 21, 28, …? (a) 70 (b) 77 (c) 71 (d) 63
  6. 6.What is the sum of all the whole numbers from 1 to 38? (a) 722 (b) 1482 (c) 741 (d) 703
  7. 7.Which term of the AP 18, 26, 34, 42, … is 258? (a) 33rd (b) 31st (c) 32nd (d) 30th
  8. 8.Which term of the AP 3, 11, 19, 27, … is 291? (a) 37th (b) 36th (c) 38th (d) 39th
  9. 9.What is the 31st term of the AP 4, 11, 18, 25, …? (a) 217 (b) 210 (c) 214 (d) 221
  10. 10.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 35 (b) 336 (c) 184 (d) 168
  11. 11.Which term of the AP 12, 15, 18, 21, … is 57? (a) 17th (b) 15th (c) 19th (d) 16th
  12. 12.What is the sum of the first 11 terms of the AP 8, 13, 18, …? (a) 368 (b) 58 (c) 363 (d) 726
  13. 13.What is the 18th term of the AP 8, 17, 26, 35, …? (a) 161 (b) 153 (c) 162 (d) 170
  14. 14.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 256 (c) 136 (d) 272
  15. 15.What is the sum of the first 7 terms of the AP 2, 6, 10, …? (a) 26 (b) 196 (c) 112 (d) 98
  16. 16.What is the sum of the first 7 terms of the AP 4, 8, 12, …? (a) 126 (b) 224 (c) 112 (d) 28
  17. 17.What is the sum of all the whole numbers from 1 to 49? (a) 1226 (b) 2450 (c) 1225 (d) 1176
  18. 18.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 29 (b) 170 (c) 85 (d) 100
  19. 19.What is the 34th term of the AP 10, 13, 16, 19, …? (a) 112 (b) 109 (c) 102 (d) 99
  20. 20.What is the sum of the first 8 terms of the AP 8, 14, 20, …? (a) 464 (b) 256 (c) 232 (d) 50
  21. 21.What is the 22nd term of the AP 7, 13, 19, 25, …? (a) 133 (b) 139 (c) 126 (d) 132
  22. 22.Which term of the AP 8, 14, 20, 26, … is 164? (a) 28th (b) 26th (c) 27th (d) 29th
  23. 23.What is the missing term in the AP 9, 16, 23, ?, 37? (a) 31 (b) 30 (c) 37 (d) 29
  24. 24.What is the sum of all the whole numbers from 1 to 48? (a) 2352 (b) 1128 (c) 1152 (d) 1176
  25. 25.What is the missing term in the AP 1, 4, ?, 10, 13? (a) 8 (b) 10 (c) 6 (d) 7
  26. 26.What is the 24th term of the AP 3, 10, 17, 24, …? (a) 164 (b) 171 (c) 168 (d) 161
  27. 27.What is the sum of the first 7 terms of the AP 6, 11, 16, …? (a) 294 (b) 36 (c) 147 (d) 152
  28. 28.What is the 37th term of the AP 16, 19, 22, 25, …? (a) 111 (b) 124 (c) 127 (d) 108
  29. 29.What is the 35th term of the AP 5, 13, 21, 29, …? (a) 272 (b) 277 (c) 280 (d) 285
  30. 30.What is the 21st term of the AP 10, 17, 24, 31, …? (a) 150 (b) 140 (c) 147 (d) 157
  31. 31.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 66 (c) 121 (d) 21
  32. 32.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 21 (b) 132 (c) 78 (d) 66
  33. 33.What is the missing term in the AP 10, 13, ?, 19, 22? (a) 17 (b) 16 (c) 15 (d) 19
  34. 34.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 20 (b) 150 (c) 84 (d) 75
  35. 35.What is the 18th term of the AP 3, 5, 7, 9, …? (a) 34 (b) 37 (c) 36 (d) 39
  36. 36.What is the 38th term of the AP 5, 9, 13, 17, …? (a) 152 (b) 153 (c) 157 (d) 148
  37. 37.What is the missing term in the AP 4, 13, ?, 31, 40? (a) 31 (b) 21 (c) 22 (d) 23
  38. 38.What is the 17th term of the AP 16, 23, 30, 37, …? (a) 135 (b) 112 (c) 119 (d) 128
  39. 39.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 6 (b) 40 (c) 21 (d) 20
  40. 40.Which term of the AP 9, 11, 13, 15, … is 29? (a) 13th (b) 10th (c) 11th (d) 12th

Answer key

  1. 27th
  2. 210
  3. 234
  4. 92
  5. 70
  6. 741
  7. 31st
  8. 37th
  9. 214
  10. 168
  11. 16th
  12. 363
  13. 161
  14. 256
  15. 98
  16. 112
  17. 1225
  18. 85
  19. 109
  20. 232
  21. 133
  22. 27th
  23. 30
  24. 1176
  25. 7
  26. 164
  27. 147
  28. 124
  29. 277
  30. 150
  31. 121
  32. 66
  33. 16
  34. 75
  35. 37
  36. 153
  37. 22
  38. 128
  39. 20
  40. 11th

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