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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 403 · 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 terms of the AP 3, 9, 15, …? (a) 270 (b) 486 (c) 51 (d) 243
  2. 2.What is the missing term in the AP 12, 21, 30, ?, 48? (a) 38 (b) 40 (c) 48 (d) 39
  3. 3.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 930 (c) 900 (d) 59
  4. 4.What is the sum of the first 8 terms of the AP 6, 11, 16, …? (a) 188 (b) 376 (c) 208 (d) 41
  5. 5.What is the missing term in the AP 17, 22, 27, ?, 37? (a) 32 (b) 33 (c) 31 (d) 37
  6. 6.What is the missing term in the AP 1, 6, 11, ?, 21? (a) 21 (b) 16 (c) 15 (d) 17
  7. 7.What is the 24th term of the AP 11, 18, 25, 32, …? (a) 172 (b) 179 (c) 168 (d) 161
  8. 8.Which term of the AP 10, 12, 14, 16, … is 60? (a) 26th (b) 27th (c) 25th (d) 30th
  9. 9.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 25 (c) 30 (d) 9
  10. 10.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 8 (b) 70 (c) 35 (d) 36
  11. 11.What is the missing term in the AP 20, ?, 28, 32, 36? (a) 24 (b) 28 (c) 23 (d) 25
  12. 12.What is the 21st term of the AP 20, 23, 26, 29, …? (a) 60 (b) 80 (c) 63 (d) 83
  13. 13.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 33 (c) 289 (d) 153
  14. 14.What is the 13th term of the AP 6, 13, 20, 27, …? (a) 97 (b) 91 (c) 90 (d) 84
  15. 15.Which term of the AP 14, 18, 22, 26, … is 122? (a) 30th (b) 29th (c) 28th (d) 27th
  16. 16.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 20 (b) 180 (c) 174 (d) 348
  17. 17.What is the missing term in the AP 6, 14, 22, ?, 38? (a) 38 (b) 31 (c) 29 (d) 30
  18. 18.What is the 23rd term of the AP 17, 19, 21, 23, …? (a) 46 (b) 61 (c) 63 (d) 44
  19. 19.What is the sum of all the whole numbers from 1 to 52? (a) 1326 (b) 1378 (c) 2756 (d) 1352
  20. 20.What is the 13th term of the AP 4, 9, 14, 19, …? (a) 60 (b) 64 (c) 69 (d) 65
  21. 21.What is the 27th term of the AP 3, 9, 15, 21, …? (a) 156 (b) 159 (c) 162 (d) 165
  22. 22.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 4422 (c) 2211 (d) 2145
  23. 23.What is the missing term in the AP 6, ?, 14, 18, 22? (a) 11 (b) 14 (c) 9 (d) 10
  24. 24.What is the 27th term of the AP 10, 19, 28, 37, …? (a) 253 (b) 244 (c) 234 (d) 243
  25. 25.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 558 (b) 55 (c) 306 (d) 279
  26. 26.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 55 (b) 10 (c) 60 (d) 110
  27. 27.What is the missing term in the AP 19, 21, ?, 25, 27? (a) 22 (b) 24 (c) 23 (d) 25
  28. 28.What is the 26th term of the AP 10, 19, 28, 37, …? (a) 225 (b) 234 (c) 235 (d) 244
  29. 29.Which term of the AP 6, 14, 22, 30, … is 166? (a) 21st (b) 23rd (c) 20th (d) 22nd
  30. 30.What is the 31st term of the AP 9, 13, 17, 21, …? (a) 129 (b) 133 (c) 124 (d) 120
  31. 31.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 29 (c) 120 (d) 240
  32. 32.What is the 34th term of the AP 3, 8, 13, 18, …? (a) 165 (b) 173 (c) 170 (d) 168
  33. 33.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 200 (b) 110 (c) 19 (d) 100
  34. 34.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 210 (c) 105 (d) 27
  35. 35.What is the 30th term of the AP 7, 10, 13, 16, …? (a) 94 (b) 87 (c) 90 (d) 97
  36. 36.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 104 (b) 192 (c) 19 (d) 96
  37. 37.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 70 (b) 140 (c) 85 (d) 26
  38. 38.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 135 (b) 270 (c) 27 (d) 138
  39. 39.Which term of the AP 19, 23, 27, 31, … is 139? (a) 32nd (b) 30th (c) 33rd (d) 31st
  40. 40.Which term of the AP 17, 25, 33, 41, … is 105? (a) 13th (b) 12th (c) 11th (d) 14th

Answer key

  1. 243
  2. 39
  3. 900
  4. 188
  5. 32
  6. 16
  7. 172
  8. 26th
  9. 25
  10. 35
  11. 24
  12. 80
  13. 289
  14. 90
  15. 28th
  16. 174
  17. 30
  18. 61
  19. 1378
  20. 64
  21. 159
  22. 2211
  23. 10
  24. 244
  25. 279
  26. 55
  27. 23
  28. 235
  29. 21st
  30. 129
  31. 225
  32. 168
  33. 100
  34. 196
  35. 94
  36. 96
  37. 70
  38. 135
  39. 31st
  40. 12th

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