← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 666 · 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 39th term of the AP 13, 18, 23, 28, …? (a) 190 (b) 203 (c) 208 (d) 195
  2. 2.What is the 36th term of the AP 3, 9, 15, 21, …? (a) 219 (b) 210 (c) 216 (d) 213
  3. 3.What is the sum of the first 7 terms of the AP 6, 7, 8, …? (a) 12 (b) 64 (c) 63 (d) 126
  4. 4.What is the sum of the first 11 terms of the AP 7, 12, 17, …? (a) 357 (b) 57 (c) 352 (d) 704
  5. 5.What is the sum of all the whole numbers from 1 to 46? (a) 1035 (b) 2162 (c) 1081 (d) 1058
  6. 6.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 34 (b) 210 (c) 420 (d) 228
  7. 7.What is the 16th term of the AP 2, 9, 16, 23, …? (a) 107 (b) 114 (c) 112 (d) 105
  8. 8.Which term of the AP 7, 13, 19, 25, … is 67? (a) 10th (b) 12th (c) 13th (d) 11th
  9. 9.What is the sum of all the whole numbers from 1 to 21? (a) 231 (b) 232 (c) 210 (d) 462
  10. 10.What is the missing term in the AP 14, 22, ?, 38, 46? (a) 29 (b) 31 (c) 30 (d) 38
  11. 11.What is the sum of the first 10 terms of the AP 4, 8, 12, …? (a) 240 (b) 40 (c) 220 (d) 440
  12. 12.What is the 13th term of the AP 15, 23, 31, 39, …? (a) 119 (b) 111 (c) 96 (d) 104
  13. 13.What is the missing term in the AP 15, 21, 27, ?, 39? (a) 39 (b) 34 (c) 32 (d) 33
  14. 14.What is the 26th term of the AP 17, 24, 31, 38, …? (a) 175 (b) 199 (c) 182 (d) 192
  15. 15.What is the missing term in the AP 18, ?, 34, 42, 50? (a) 34 (b) 27 (c) 26 (d) 25
  16. 16.What is the 29th term of the AP 19, 23, 27, 31, …? (a) 131 (b) 135 (c) 112 (d) 116
  17. 17.What is the sum of the first 12 terms of the AP 3, 5, 7, …? (a) 180 (b) 25 (c) 336 (d) 168
  18. 18.What is the missing term in the AP 8, ?, 26, 35, 44? (a) 16 (b) 26 (c) 18 (d) 17
  19. 19.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 552 (c) 45 (d) 276
  20. 20.What is the 30th term of the AP 5, 11, 17, 23, …? (a) 185 (b) 179 (c) 174 (d) 180
  21. 21.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 21 (b) 132 (c) 78 (d) 66
  22. 22.What is the missing term in the AP 11, 17, ?, 29, 35? (a) 23 (b) 24 (c) 22 (d) 29
  23. 23.Which term of the AP 18, 22, 26, 30, … is 74? (a) 15th (b) 14th (c) 17th (d) 16th
  24. 24.What is the 34th term of the AP 10, 17, 24, 31, …? (a) 241 (b) 231 (c) 238 (d) 248
  25. 25.Which term of the AP 13, 21, 29, 37, … is 253? (a) 33rd (b) 30th (c) 31st (d) 32nd
  26. 26.What is the 17th term of the AP 4, 6, 8, 10, …? (a) 38 (b) 36 (c) 32 (d) 34
  27. 27.What is the missing term in the AP 19, ?, 27, 31, 35? (a) 23 (b) 27 (c) 24 (d) 22
  28. 28.What is the 11th term of the AP 15, 23, 31, 39, …? (a) 95 (b) 88 (c) 80 (d) 103
  29. 29.What is the missing term in the AP 4, 13, ?, 31, 40? (a) 23 (b) 22 (c) 21 (d) 31
  30. 30.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 171 (b) 33 (c) 153 (d) 306
  31. 31.What is the sum of all the whole numbers from 1 to 95? (a) 4561 (b) 9120 (c) 4560 (d) 4465
  32. 32.What is the 31st term of the AP 12, 17, 22, 27, …? (a) 162 (b) 150 (c) 167 (d) 155
  33. 33.What is the sum of all the whole numbers from 1 to 36? (a) 1332 (b) 666 (c) 630 (d) 648
  34. 34.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 350 (b) 380 (c) 62 (d) 700
  35. 35.What is the sum of the first 10 terms of the AP 5, 11, 17, …? (a) 640 (b) 59 (c) 350 (d) 320
  36. 36.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 28 (c) 56 (d) 49
  37. 37.What is the 23rd term of the AP 5, 7, 9, 11, …? (a) 51 (b) 46 (c) 49 (d) 44
  38. 38.What is the sum of the first 8 terms of the AP 10, 13, 16, …? (a) 328 (b) 176 (c) 164 (d) 31
  39. 39.What is the 39th term of the AP 13, 16, 19, 22, …? (a) 117 (b) 114 (c) 130 (d) 127
  40. 40.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 36 (c) 64 (d) 72

Answer key

  1. 203
  2. 213
  3. 63
  4. 352
  5. 1081
  6. 210
  7. 107
  8. 11th
  9. 231
  10. 30
  11. 220
  12. 111
  13. 33
  14. 192
  15. 26
  16. 131
  17. 168
  18. 17
  19. 529
  20. 179
  21. 66
  22. 23
  23. 15th
  24. 241
  25. 31st
  26. 36
  27. 23
  28. 95
  29. 22
  30. 153
  31. 4560
  32. 162
  33. 666
  34. 350
  35. 320
  36. 49
  37. 49
  38. 164
  39. 127
  40. 64

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