← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 152 · 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 all the whole numbers from 1 to 63? (a) 4032 (b) 2017 (c) 1953 (d) 2016
  2. 2.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 65 (b) 19 (c) 110 (d) 55
  3. 3.What is the missing term in the AP 4, ?, 10, 13, 16? (a) 6 (b) 8 (c) 10 (d) 7
  4. 4.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 34 (b) 228 (c) 210 (d) 420
  5. 5.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 380 (c) 37 (d) 190
  6. 6.Which term of the AP 16, 23, 30, 37, … is 79? (a) 11th (b) 10th (c) 12th (d) 9th
  7. 7.What is the missing term in the AP 1, 7, ?, 19, 25? (a) 12 (b) 14 (c) 13 (d) 19
  8. 8.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 78 (c) 156 (d) 144
  9. 9.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 400 (d) 39
  10. 10.What is the sum of all the whole numbers from 1 to 15? (a) 121 (b) 120 (c) 240 (d) 105
  11. 11.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 506 (c) 43 (d) 253
  12. 12.What is the sum of the first 6 terms of the AP 6, 9, 12, …? (a) 162 (b) 90 (c) 21 (d) 81
  13. 13.What is the 40th term of the AP 20, 29, 38, 47, …? (a) 360 (b) 351 (c) 371 (d) 380
  14. 14.What is the 10th term of the AP 12, 15, 18, 21, …? (a) 42 (b) 27 (c) 39 (d) 30
  15. 15.What is the missing term in the AP 12, 21, 30, ?, 48? (a) 48 (b) 38 (c) 39 (d) 40
  16. 16.What is the 14th term of the AP 2, 4, 6, 8, …? (a) 29 (b) 26 (c) 30 (d) 28
  17. 17.What is the 30th term of the AP 14, 18, 22, 26, …? (a) 130 (b) 134 (c) 120 (d) 116
  18. 18.What is the 25th term of the AP 4, 10, 16, 22, …? (a) 144 (b) 148 (c) 154 (d) 150
  19. 19.What is the 18th term of the AP 4, 8, 12, 16, …? (a) 76 (b) 72 (c) 68 (d) 73
  20. 20.What is the missing term in the AP 10, 14, 18, ?, 26? (a) 21 (b) 22 (c) 23 (d) 26
  21. 21.What is the missing term in the AP 6, 15, 24, ?, 42? (a) 42 (b) 34 (c) 33 (d) 32
  22. 22.What is the 19th term of the AP 2, 4, 6, 8, …? (a) 39 (b) 36 (c) 40 (d) 38
  23. 23.What is the 15th term of the AP 6, 12, 18, 24, …? (a) 91 (b) 84 (c) 90 (d) 96
  24. 24.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 324 (c) 171 (d) 342
  25. 25.What is the 40th term of the AP 3, 10, 17, 24, …? (a) 273 (b) 283 (c) 280 (d) 276
  26. 26.Which term of the AP 7, 15, 23, 31, … is 95? (a) 12th (b) 13th (c) 11th (d) 14th
  27. 27.What is the 15th term of the AP 15, 22, 29, 36, …? (a) 105 (b) 113 (c) 98 (d) 120
  28. 28.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 110 (c) 50 (d) 55
  29. 29.What is the sum of all the whole numbers from 1 to 64? (a) 2048 (b) 2016 (c) 4160 (d) 2080
  30. 30.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 23 (b) 156 (c) 144 (d) 288
  31. 31.What is the sum of the first 10 terms of the AP 10, 16, 22, …? (a) 370 (b) 400 (c) 740 (d) 64
  32. 32.What is the missing term in the AP 4, 7, ?, 13, 16? (a) 9 (b) 13 (c) 11 (d) 10
  33. 33.Which term of the AP 5, 12, 19, 26, … is 68? (a) 9th (b) 10th (c) 12th (d) 11th
  34. 34.Which term of the AP 9, 11, 13, 15, … is 77? (a) 34th (b) 36th (c) 37th (d) 35th
  35. 35.What is the sum of all the whole numbers from 1 to 80? (a) 3160 (b) 3200 (c) 6480 (d) 3240
  36. 36.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 325 (c) 625 (d) 49
  37. 37.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 27 (c) 196 (d) 210
  38. 38.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 15 (c) 25 (d) 9
  39. 39.What is the missing term in the AP 12, 19, 26, ?, 40? (a) 32 (b) 34 (c) 33 (d) 40
  40. 40.What is the 18th term of the AP 16, 23, 30, 37, …? (a) 135 (b) 119 (c) 126 (d) 142

Answer key

  1. 2016
  2. 55
  3. 7
  4. 210
  5. 361
  6. 10th
  7. 13
  8. 144
  9. 400
  10. 120
  11. 484
  12. 81
  13. 371
  14. 39
  15. 39
  16. 28
  17. 130
  18. 148
  19. 72
  20. 22
  21. 33
  22. 38
  23. 90
  24. 324
  25. 276
  26. 12th
  27. 113
  28. 55
  29. 2080
  30. 144
  31. 370
  32. 10
  33. 10th
  34. 35th
  35. 3240
  36. 625
  37. 196
  38. 25
  39. 33
  40. 135

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