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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 996 · 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 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 812 (c) 55 (d) 784
  2. 2.What is the sum of the first 11 terms of the AP 9, 12, 15, …? (a) 264 (b) 528 (c) 267 (d) 39
  3. 3.What is the sum of the first 11 terms of the AP 1, 4, 7, …? (a) 31 (b) 352 (c) 176 (d) 179
  4. 4.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 81 (c) 17 (d) 90
  5. 5.What is the 18th term of the AP 7, 16, 25, 34, …? (a) 162 (b) 160 (c) 169 (d) 153
  6. 6.Which term of the AP 5, 11, 17, 23, … is 53? (a) 10th (b) 8th (c) 9th (d) 11th
  7. 7.What is the missing term in the AP 10, 14, 18, ?, 26? (a) 26 (b) 23 (c) 21 (d) 22
  8. 8.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 30 (c) 15 (d) 9
  9. 9.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 109 (b) 108 (c) 16 (d) 216
  10. 10.What is the 30th term of the AP 1, 9, 17, 25, …? (a) 240 (b) 241 (c) 233 (d) 232
  11. 11.What is the sum of the first 10 terms of the AP 10, 15, 20, …? (a) 350 (b) 55 (c) 325 (d) 650
  12. 12.Which term of the AP 1, 5, 9, 13, … is 73? (a) 21st (b) 19th (c) 18th (d) 20th
  13. 13.What is the sum of the first 12 terms of the AP 2, 4, 6, …? (a) 312 (b) 156 (c) 168 (d) 24
  14. 14.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 37 (b) 150 (c) 132 (d) 264
  15. 15.What is the 36th term of the AP 6, 9, 12, 15, …? (a) 105 (b) 108 (c) 111 (d) 114
  16. 16.What is the sum of all the whole numbers from 1 to 84? (a) 7140 (b) 3570 (c) 3528 (d) 3486
  17. 17.What is the 23rd term of the AP 19, 26, 33, 40, …? (a) 180 (b) 154 (c) 161 (d) 173
  18. 18.What is the sum of the first 11 terms of the AP 8, 12, 16, …? (a) 308 (b) 330 (c) 616 (d) 48
  19. 19.What is the 22nd term of the AP 13, 15, 17, 19, …? (a) 42 (b) 55 (c) 57 (d) 44
  20. 20.What is the sum of the first 5 terms of the AP 7, 12, 17, …? (a) 90 (b) 27 (c) 85 (d) 170
  21. 21.What is the 17th term of the AP 20, 22, 24, 26, …? (a) 54 (b) 32 (c) 34 (d) 52
  22. 22.What is the 17th term of the AP 18, 27, 36, 45, …? (a) 153 (b) 171 (c) 144 (d) 162
  23. 23.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 102 (b) 120 (c) 204 (d) 32
  24. 24.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 5 (b) 30 (c) 15 (d) 16
  25. 25.What is the 26th term of the AP 14, 22, 30, 38, …? (a) 222 (b) 214 (c) 200 (d) 208
  26. 26.What is the 10th term of the AP 1, 9, 17, 25, …? (a) 81 (b) 72 (c) 73 (d) 80
  27. 27.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 60 (b) 8 (c) 30 (d) 31
  28. 28.Which term of the AP 1, 4, 7, 10, … is 97? (a) 34th (b) 33rd (c) 35th (d) 32nd
  29. 29.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 190 (c) 37 (d) 380
  30. 30.What is the 34th term of the AP 11, 19, 27, 35, …? (a) 275 (b) 283 (c) 272 (d) 264
  31. 31.Which term of the AP 13, 16, 19, 22, … is 85? (a) 25th (b) 27th (c) 24th (d) 26th
  32. 32.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 306 (c) 154 (d) 136
  33. 33.What is the 21st term of the AP 12, 20, 28, 36, …? (a) 180 (b) 172 (c) 168 (d) 160
  34. 34.What is the sum of all the whole numbers from 1 to 76? (a) 2850 (b) 5852 (c) 2888 (d) 2926
  35. 35.What is the 33rd term of the AP 20, 24, 28, 32, …? (a) 132 (b) 152 (c) 128 (d) 148
  36. 36.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 325 (c) 625 (d) 650
  37. 37.What is the 20th term of the AP 20, 24, 28, 32, …? (a) 80 (b) 96 (c) 76 (d) 100
  38. 38.What is the missing term in the AP 16, 19, 22, ?, 28? (a) 24 (b) 25 (c) 28 (d) 26
  39. 39.What is the sum of the first 7 terms of the AP 3, 6, 9, …? (a) 84 (b) 87 (c) 21 (d) 168
  40. 40.What is the 24th term of the AP 10, 12, 14, 16, …? (a) 48 (b) 46 (c) 56 (d) 58

Answer key

  1. 784
  2. 264
  3. 176
  4. 81
  5. 160
  6. 9th
  7. 22
  8. 25
  9. 108
  10. 233
  11. 325
  12. 19th
  13. 156
  14. 132
  15. 111
  16. 3570
  17. 173
  18. 308
  19. 55
  20. 85
  21. 52
  22. 162
  23. 102
  24. 15
  25. 214
  26. 73
  27. 30
  28. 33rd
  29. 361
  30. 275
  31. 25th
  32. 153
  33. 172
  34. 2926
  35. 148
  36. 625
  37. 96
  38. 25
  39. 84
  40. 56

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