Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 534 · 40 questions

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.

1. 1.What is the 31st term of the AP 1, 5, 9, 13, …? (a) 120 (b) 121 (c) 124 (d) 125
2. 2.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 70 (b) 65 (c) 130 (d) 17
3. 3.What is the 17th term of the AP 15, 19, 23, 27, …? (a) 83 (b) 68 (c) 64 (d) 79
4. 4.What is the sum of the first 8 terms of the AP 7, 13, 19, …? (a) 49 (b) 448 (c) 224 (d) 248
5. 5.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 10 (b) 12 (c) 13 (d) 11
6. 6.What is the 18th term of the AP 13, 21, 29, 37, …? (a) 144 (b) 149 (c) 136 (d) 157
7. 7.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 552 (c) 45 (d) 529
8. 8.What is the 13th term of the AP 19, 24, 29, 34, …? (a) 60 (b) 79 (c) 84 (d) 65
9. 9.What is the 17th term of the AP 5, 9, 13, 17, …? (a) 73 (b) 68 (c) 64 (d) 69
10. 10.What is the 23rd term of the AP 14, 20, 26, 32, …? (a) 138 (b) 152 (c) 146 (d) 132
11. 11.What is the missing term in the AP 18, ?, 26, 30, 34? (a) 26 (b) 22 (c) 23 (d) 21
12. 12.What is the 22nd term of the AP 17, 26, 35, 44, …? (a) 206 (b) 198 (c) 189 (d) 215
13. 13.What is the missing term in the AP 15, ?, 27, 33, 39? (a) 21 (b) 22 (c) 27 (d) 20
14. 14.What is the 13th term of the AP 9, 12, 15, 18, …? (a) 45 (b) 36 (c) 48 (d) 39
15. 15.Which term of the AP 15, 17, 19, 21, … is 55? (a) 22nd (b) 23rd (c) 20th (d) 21st
16. 16.What is the 16th term of the AP 1, 3, 5, 7, …? (a) 31 (b) 33 (c) 32 (d) 30
17. 17.What is the 25th term of the AP 8, 14, 20, 26, …? (a) 150 (b) 144 (c) 158 (d) 152
18. 18.Which term of the AP 18, 23, 28, 33, … is 203? (a) 40th (b) 38th (c) 39th (d) 37th
19. 19.What is the missing term in the AP 12, 20, 28, ?, 44? (a) 44 (b) 35 (c) 37 (d) 36
20. 20.What is the missing term in the AP 13, ?, 21, 25, 29? (a) 17 (b) 21 (c) 18 (d) 16
21. 21.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 506 (b) 275 (c) 253 (d) 43
22. 22.What is the missing term in the AP 18, 24, 30, ?, 42? (a) 35 (b) 42 (c) 36 (d) 37
23. 23.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 13 (c) 49 (d) 56
24. 24.What is the 30th term of the AP 10, 15, 20, 25, …? (a) 150 (b) 160 (c) 145 (d) 155
25. 25.What is the 29th term of the AP 6, 13, 20, 27, …? (a) 203 (b) 202 (c) 209 (d) 196
26. 26.Which term of the AP 7, 14, 21, 28, … is 98? (a) 13th (b) 15th (c) 14th (d) 16th
27. 27.What is the sum of the first 9 terms of the AP 1, 4, 7, …? (a) 120 (b) 234 (c) 117 (d) 25
28. 28.What is the missing term in the AP 12, 18, ?, 30, 36? (a) 23 (b) 25 (c) 24 (d) 30
29. 29.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 68 (b) 19 (c) 65 (d) 130
30. 30.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 64 (b) 120 (c) 11 (d) 60
31. 31.What is the missing term in the AP 13, 17, 21, ?, 29? (a) 24 (b) 26 (c) 29 (d) 25
32. 32.What is the 24th term of the AP 8, 16, 24, 32, …? (a) 193 (b) 192 (c) 184 (d) 200
33. 33.Which term of the AP 3, 7, 11, 15, … is 55? (a) 13th (b) 16th (c) 14th (d) 15th
34. 34.What is the sum of all the whole numbers from 1 to 68? (a) 2278 (b) 2312 (c) 4692 (d) 2346
35. 35.Which term of the AP 17, 21, 25, 29, … is 149? (a) 36th (b) 34th (c) 35th (d) 33rd
36. 36.What is the 24th term of the AP 6, 8, 10, 12, …? (a) 54 (b) 48 (c) 52 (d) 46
37. 37.Which term of the AP 2, 5, 8, 11, … is 83? (a) 29th (b) 27th (c) 28th (d) 30th
38. 38.What is the missing term in the AP 1, 8, 15, ?, 29? (a) 29 (b) 22 (c) 23 (d) 21
39. 39.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 5000 (c) 10100 (d) 5050
40. 40.What is the 34th term of the AP 19, 27, 35, 43, …? (a) 264 (b) 272 (c) 291 (d) 283

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