← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 817 · 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 2, 4, 6, …? (a) 99 (b) 90 (c) 180 (d) 18
  2. 2.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 21 (b) 132 (c) 242 (d) 121
  3. 3.What is the 25th term of the AP 5, 11, 17, 23, …? (a) 149 (b) 150 (c) 155 (d) 144
  4. 4.What is the sum of the first 7 terms of the AP 10, 16, 22, …? (a) 217 (b) 46 (c) 196 (d) 392
  5. 5.What is the missing term in the AP 12, 20, ?, 36, 44? (a) 27 (b) 29 (c) 28 (d) 36
  6. 6.What is the 38th term of the AP 1, 5, 9, 13, …? (a) 152 (b) 153 (c) 148 (d) 149
  7. 7.Which term of the AP 7, 15, 23, 31, … is 119? (a) 16th (b) 14th (c) 17th (d) 15th
  8. 8.Which term of the AP 16, 24, 32, 40, … is 256? (a) 33rd (b) 30th (c) 32nd (d) 31st
  9. 9.What is the 22nd term of the AP 1, 7, 13, 19, …? (a) 133 (b) 132 (c) 127 (d) 126
  10. 10.What is the 35th term of the AP 20, 27, 34, 41, …? (a) 265 (b) 238 (c) 245 (d) 258
  11. 11.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 10 (b) 52 (c) 104 (d) 56
  12. 12.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 21 (c) 121 (d) 132
  13. 13.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 784 (c) 55 (d) 406
  14. 14.What is the 14th term of the AP 18, 20, 22, 24, …? (a) 28 (b) 26 (c) 44 (d) 46
  15. 15.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 66 (b) 67 (c) 132 (d) 11
  16. 16.Which term of the AP 20, 25, 30, 35, … is 180? (a) 36th (b) 32nd (c) 33rd (d) 34th
  17. 17.What is the 15th term of the AP 12, 14, 16, 18, …? (a) 30 (b) 40 (c) 28 (d) 42
  18. 18.Which term of the AP 5, 8, 11, 14, … is 26? (a) 8th (b) 9th (c) 7th (d) 10th
  19. 19.What is the 37th term of the AP 18, 26, 34, 42, …? (a) 288 (b) 306 (c) 314 (d) 296
  20. 20.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 144 (c) 23 (d) 156
  21. 21.What is the sum of all the whole numbers from 1 to 30? (a) 450 (b) 465 (c) 930 (d) 435
  22. 22.What is the sum of all the whole numbers from 1 to 68? (a) 4692 (b) 2346 (c) 2278 (d) 2312
  23. 23.What is the 28th term of the AP 16, 24, 32, 40, …? (a) 240 (b) 224 (c) 216 (d) 232
  24. 24.What is the 37th term of the AP 7, 10, 13, 16, …? (a) 111 (b) 108 (c) 115 (d) 118
  25. 25.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 12 (b) 154 (c) 77 (d) 78
  26. 26.What is the sum of the first 9 terms of the AP 4, 9, 14, …? (a) 432 (b) 44 (c) 221 (d) 216
  27. 27.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 529 (c) 45 (d) 552
  28. 28.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 420 (b) 228 (c) 210 (d) 34
  29. 29.What is the sum of the first 12 terms of the AP 5, 8, 11, …? (a) 38 (b) 276 (c) 258 (d) 516
  30. 30.What is the sum of all the whole numbers from 1 to 53? (a) 1431 (b) 1378 (c) 2862 (d) 1432
  31. 31.What is the 29th term of the AP 1, 5, 9, 13, …? (a) 116 (b) 113 (c) 117 (d) 112
  32. 32.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 45 (c) 17 (d) 90
  33. 33.What is the sum of the first 5 terms of the AP 8, 12, 16, …? (a) 160 (b) 24 (c) 80 (d) 90
  34. 34.What is the 31st term of the AP 12, 20, 28, 36, …? (a) 260 (b) 248 (c) 240 (d) 252
  35. 35.What is the 24th term of the AP 9, 11, 13, 15, …? (a) 48 (b) 57 (c) 55 (d) 46
  36. 36.What is the missing term in the AP 19, ?, 29, 34, 39? (a) 24 (b) 23 (c) 29 (d) 25
  37. 37.What is the sum of all the whole numbers from 1 to 78? (a) 3003 (b) 6162 (c) 3042 (d) 3081
  38. 38.What is the 33rd term of the AP 8, 17, 26, 35, …? (a) 296 (b) 305 (c) 288 (d) 297
  39. 39.What is the 10th term of the AP 6, 14, 22, 30, …? (a) 72 (b) 80 (c) 86 (d) 78
  40. 40.What is the sum of the first 10 terms of the AP 5, 6, 7, …? (a) 190 (b) 14 (c) 100 (d) 95

Answer key

  1. 90
  2. 121
  3. 149
  4. 196
  5. 28
  6. 149
  7. 15th
  8. 31st
  9. 127
  10. 258
  11. 52
  12. 121
  13. 784
  14. 44
  15. 66
  16. 33rd
  17. 40
  18. 8th
  19. 306
  20. 144
  21. 465
  22. 2346
  23. 232
  24. 115
  25. 77
  26. 216
  27. 529
  28. 210
  29. 258
  30. 1431
  31. 113
  32. 81
  33. 80
  34. 252
  35. 55
  36. 24
  37. 3081
  38. 296
  39. 78
  40. 95

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad