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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 61 · 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 33rd term of the AP 19, 23, 27, 31, …? (a) 151 (b) 132 (c) 147 (d) 128
  2. 2.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 169 (c) 91 (d) 182
  3. 3.What is the 27th term of the AP 15, 23, 31, 39, …? (a) 231 (b) 208 (c) 223 (d) 216
  4. 4.What is the sum of all the whole numbers from 1 to 42? (a) 882 (b) 1806 (c) 903 (d) 861
  5. 5.Which term of the AP 12, 15, 18, 21, … is 45? (a) 13th (b) 11th (c) 12th (d) 15th
  6. 6.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 185 (b) 32 (c) 200 (d) 370
  7. 7.What is the sum of all the whole numbers from 1 to 86? (a) 3698 (b) 3741 (c) 7482 (d) 3655
  8. 8.What is the missing term in the AP 19, 21, ?, 25, 27? (a) 25 (b) 23 (c) 22 (d) 24
  9. 9.What is the missing term in the AP 6, 11, 16, ?, 26? (a) 26 (b) 22 (c) 20 (d) 21
  10. 10.What is the sum of all the whole numbers from 1 to 52? (a) 1352 (b) 1378 (c) 1326 (d) 2756
  11. 11.What is the sum of all the whole numbers from 1 to 76? (a) 2850 (b) 5852 (c) 2926 (d) 2888
  12. 12.What is the sum of all the whole numbers from 1 to 30? (a) 435 (b) 465 (c) 450 (d) 930
  13. 13.What is the 39th term of the AP 15, 21, 27, 33, …? (a) 234 (b) 243 (c) 228 (d) 249
  14. 14.What is the 10th term of the AP 15, 18, 21, 24, …? (a) 30 (b) 27 (c) 45 (d) 42
  15. 15.What is the 14th term of the AP 10, 14, 18, 22, …? (a) 66 (b) 52 (c) 56 (d) 62
  16. 16.What is the 38th term of the AP 4, 7, 10, 13, …? (a) 114 (b) 115 (c) 118 (d) 111
  17. 17.What is the missing term in the AP 12, 16, ?, 24, 28? (a) 21 (b) 19 (c) 24 (d) 20
  18. 18.What is the sum of the first 9 terms of the AP 10, 15, 20, …? (a) 540 (b) 275 (c) 50 (d) 270
  19. 19.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 144 (b) 136 (c) 272 (d) 24
  20. 20.What is the 27th term of the AP 3, 9, 15, 21, …? (a) 162 (b) 165 (c) 156 (d) 159
  21. 21.What is the sum of the first 9 terms of the AP 8, 13, 18, …? (a) 257 (b) 504 (c) 48 (d) 252
  22. 22.What is the missing term in the AP 13, 21, 29, ?, 45? (a) 36 (b) 38 (c) 37 (d) 45
  23. 23.What is the 23rd term of the AP 11, 19, 27, 35, …? (a) 187 (b) 195 (c) 176 (d) 184
  24. 24.What is the 20th term of the AP 14, 20, 26, 32, …? (a) 134 (b) 128 (c) 120 (d) 114
  25. 25.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 66 (c) 132 (d) 121
  26. 26.Which term of the AP 17, 24, 31, 38, … is 192? (a) 26th (b) 27th (c) 28th (d) 25th
  27. 27.What is the sum of the first 7 terms of the AP 9, 11, 13, …? (a) 21 (b) 210 (c) 112 (d) 105
  28. 28.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 380 (c) 361 (d) 37
  29. 29.What is the sum of all the whole numbers from 1 to 84? (a) 3486 (b) 3528 (c) 3570 (d) 7140
  30. 30.What is the 39th term of the AP 3, 7, 11, 15, …? (a) 159 (b) 152 (c) 156 (d) 155
  31. 31.Which term of the AP 15, 18, 21, 24, … is 102? (a) 30th (b) 29th (c) 31st (d) 34th
  32. 32.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 140 (b) 24 (c) 70 (d) 75
  33. 33.Which term of the AP 4, 9, 14, 19, … is 134? (a) 26th (b) 29th (c) 27th (d) 28th
  34. 34.Which term of the AP 18, 20, 22, 24, … is 50? (a) 18th (b) 16th (c) 17th (d) 25th
  35. 35.What is the sum of all the whole numbers from 1 to 34? (a) 595 (b) 1190 (c) 561 (d) 578
  36. 36.What is the 22nd term of the AP 5, 10, 15, 20, …? (a) 111 (b) 115 (c) 105 (d) 110
  37. 37.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 91 (b) 16 (c) 92 (d) 182
  38. 38.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 15 (c) 9 (d) 25
  39. 39.What is the 12th term of the AP 10, 13, 16, 19, …? (a) 33 (b) 43 (c) 36 (d) 46
  40. 40.Which term of the AP 3, 6, 9, 12, … is 63? (a) 23rd (b) 20th (c) 22nd (d) 21st

Answer key

  1. 147
  2. 169
  3. 223
  4. 903
  5. 12th
  6. 185
  7. 3741
  8. 23
  9. 21
  10. 1378
  11. 2926
  12. 465
  13. 243
  14. 42
  15. 62
  16. 115
  17. 20
  18. 270
  19. 136
  20. 159
  21. 252
  22. 37
  23. 187
  24. 128
  25. 121
  26. 26th
  27. 105
  28. 361
  29. 3570
  30. 155
  31. 30th
  32. 70
  33. 27th
  34. 17th
  35. 595
  36. 110
  37. 91
  38. 25
  39. 43
  40. 21st

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