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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 457 · 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 7, 9, 11, …? (a) 144 (b) 135 (c) 270 (d) 23
  2. 2.What is the 31st term of the AP 2, 10, 18, 26, …? (a) 240 (b) 242 (c) 248 (d) 250
  3. 3.What is the sum of the first 12 terms of the AP 7, 10, 13, …? (a) 40 (b) 300 (c) 564 (d) 282
  4. 4.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 182 (c) 169 (d) 25
  5. 5.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 31 (c) 272 (d) 256
  6. 6.What is the sum of all the whole numbers from 1 to 34? (a) 1190 (b) 561 (c) 595 (d) 578
  7. 7.What is the sum of all the whole numbers from 1 to 15? (a) 120 (b) 105 (c) 121 (d) 240
  8. 8.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 80 (b) 12 (c) 45 (d) 40
  9. 9.What is the 18th term of the AP 15, 24, 33, 42, …? (a) 162 (b) 153 (c) 168 (d) 177
  10. 10.What is the 27th term of the AP 6, 14, 22, 30, …? (a) 208 (b) 214 (c) 216 (d) 222
  11. 11.What is the sum of the first 9 terms of the AP 8, 11, 14, …? (a) 183 (b) 180 (c) 32 (d) 360
  12. 12.What is the sum of all the whole numbers from 1 to 70? (a) 2415 (b) 2450 (c) 4970 (d) 2485
  13. 13.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 10 (b) 80 (c) 40 (d) 41
  14. 14.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 729 (c) 53 (d) 378
  15. 15.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 992 (c) 497 (d) 496
  16. 16.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 484 (c) 506 (d) 253
  17. 17.What is the 31st term of the AP 1, 8, 15, 22, …? (a) 210 (b) 218 (c) 217 (d) 211
  18. 18.Which term of the AP 1, 5, 9, 13, … is 65? (a) 17th (b) 19th (c) 16th (d) 18th
  19. 19.What is the 26th term of the AP 17, 24, 31, 38, …? (a) 175 (b) 199 (c) 182 (d) 192
  20. 20.What is the 18th term of the AP 18, 22, 26, 30, …? (a) 90 (b) 86 (c) 68 (d) 72
  21. 21.What is the sum of all the whole numbers from 1 to 91? (a) 4187 (b) 4095 (c) 4186 (d) 8372
  22. 22.What is the 15th term of the AP 10, 13, 16, 19, …? (a) 55 (b) 45 (c) 52 (d) 42
  23. 23.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 13 (b) 96 (c) 48 (d) 54
  24. 24.What is the 21st term of the AP 14, 21, 28, 35, …? (a) 154 (b) 140 (c) 161 (d) 147
  25. 25.What is the 10th term of the AP 10, 18, 26, 34, …? (a) 72 (b) 82 (c) 90 (d) 80
  26. 26.What is the 27th term of the AP 14, 23, 32, 41, …? (a) 257 (b) 234 (c) 248 (d) 243
  27. 27.What is the 21st term of the AP 2, 6, 10, 14, …? (a) 86 (b) 82 (c) 80 (d) 84
  28. 28.What is the 28th term of the AP 9, 16, 23, 30, …? (a) 198 (b) 205 (c) 189 (d) 196
  29. 29.Which term of the AP 1, 5, 9, 13, … is 37? (a) 11th (b) 9th (c) 10th (d) 12th
  30. 30.What is the sum of the first 9 terms of the AP 6, 12, 18, …? (a) 540 (b) 54 (c) 270 (d) 297
  31. 31.What is the sum of all the whole numbers from 1 to 44? (a) 968 (b) 990 (c) 946 (d) 1980
  32. 32.What is the 18th term of the AP 5, 11, 17, 23, …? (a) 102 (b) 113 (c) 108 (d) 107
  33. 33.Which term of the AP 19, 26, 33, 40, … is 166? (a) 24th (b) 22nd (c) 23rd (d) 21st
  34. 34.What is the sum of the first 7 terms of the AP 2, 7, 12, …? (a) 238 (b) 119 (c) 124 (d) 32
  35. 35.Which term of the AP 2, 10, 18, 26, … is 122? (a) 17th (b) 16th (c) 15th (d) 18th
  36. 36.What is the 11th term of the AP 16, 22, 28, 34, …? (a) 82 (b) 60 (c) 66 (d) 76
  37. 37.Which term of the AP 7, 12, 17, 22, … is 132? (a) 26th (b) 27th (c) 25th (d) 28th
  38. 38.What is the 28th term of the AP 11, 20, 29, 38, …? (a) 243 (b) 252 (c) 254 (d) 263
  39. 39.What is the 34th term of the AP 9, 18, 27, 36, …? (a) 297 (b) 315 (c) 306 (d) 307
  40. 40.What is the 37th term of the AP 8, 14, 20, 26, …? (a) 222 (b) 224 (c) 230 (d) 216

Answer key

  1. 135
  2. 242
  3. 282
  4. 169
  5. 256
  6. 595
  7. 120
  8. 40
  9. 168
  10. 214
  11. 180
  12. 2485
  13. 40
  14. 729
  15. 496
  16. 484
  17. 211
  18. 17th
  19. 192
  20. 86
  21. 4186
  22. 52
  23. 48
  24. 154
  25. 82
  26. 248
  27. 82
  28. 198
  29. 10th
  30. 270
  31. 990
  32. 107
  33. 22nd
  34. 119
  35. 16th
  36. 76
  37. 26th
  38. 254
  39. 306
  40. 224

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