Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 423 · 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 38th term of the AP 6, 11, 16, 21, …? (a) 191 (b) 185 (c) 196 (d) 190
2. 2.What is the sum of all the whole numbers from 1 to 96? (a) 4560 (b) 9312 (c) 4656 (d) 4608
3. 3.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 24 (b) 99 (c) 198 (d) 108
4. 4.What is the sum of all the whole numbers from 1 to 41? (a) 820 (b) 1722 (c) 861 (d) 862
5. 5.What is the 21st term of the AP 1, 9, 17, 25, …? (a) 169 (b) 161 (c) 160 (d) 168
6. 6.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 17 (b) 114 (c) 66 (d) 57
7. 7.What is the sum of all the whole numbers from 1 to 85? (a) 7310 (b) 3656 (c) 3570 (d) 3655
8. 8.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 65 (b) 130 (c) 19 (d) 68
9. 9.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 576 (c) 300 (d) 47
10. 10.What is the sum of all the whole numbers from 1 to 87? (a) 7656 (b) 3741 (c) 3829 (d) 3828
11. 11.What is the 25th term of the AP 11, 13, 15, 17, …? (a) 48 (b) 61 (c) 59 (d) 50
12. 12.What is the 13th term of the AP 14, 18, 22, 26, …? (a) 66 (b) 52 (c) 62 (d) 48
13. 13.What is the missing term in the AP 12, 14, 16, ?, 20? (a) 17 (b) 18 (c) 20 (d) 19
14. 14.What is the missing term in the AP 5, 12, ?, 26, 33? (a) 18 (b) 26 (c) 19 (d) 20
15. 15.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 11 (c) 42 (d) 36
16. 16.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 96 (b) 174 (c) 22 (d) 87
17. 17.What is the missing term in the AP 4, ?, 20, 28, 36? (a) 20 (b) 13 (c) 11 (d) 12
18. 18.What is the sum of all the whole numbers from 1 to 53? (a) 1378 (b) 1431 (c) 1432 (d) 2862
19. 19.What is the sum of all the whole numbers from 1 to 67? (a) 2211 (b) 2279 (c) 4556 (d) 2278
20. 20.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 235 (b) 260 (c) 46 (d) 470
21. 21.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 289 (c) 306 (d) 153
22. 22.What is the 21st term of the AP 18, 27, 36, 45, …? (a) 180 (b) 198 (c) 207 (d) 189
23. 23.What is the sum of all the whole numbers from 1 to 99? (a) 9900 (b) 4950 (c) 4951 (d) 4851
24. 24.What is the 21st term of the AP 9, 13, 17, 21, …? (a) 89 (b) 93 (c) 84 (d) 80
25. 25.What is the sum of all the whole numbers from 1 to 44? (a) 1980 (b) 946 (c) 968 (d) 990
26. 26.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 228 (b) 432 (c) 216 (d) 29
27. 27.What is the 31st term of the AP 20, 28, 36, 44, …? (a) 268 (b) 240 (c) 260 (d) 248
28. 28.What is the missing term in the AP 1, ?, 11, 16, 21? (a) 5 (b) 11 (c) 7 (d) 6
29. 29.Which term of the AP 5, 12, 19, 26, … is 152? (a) 22nd (b) 21st (c) 24th (d) 23rd
30. 30.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 435 (c) 870 (d) 841
31. 31.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 496 (c) 465 (d) 497
32. 32.What is the sum of the first 10 terms of the AP 3, 8, 13, …? (a) 280 (b) 48 (c) 510 (d) 255
33. 33.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 21 (c) 66 (d) 132
34. 34.What is the 26th term of the AP 7, 16, 25, 34, …? (a) 232 (b) 234 (c) 225 (d) 241
35. 35.What is the missing term in the AP 2, ?, 14, 20, 26? (a) 9 (b) 14 (c) 7 (d) 8
36. 36.Which term of the AP 17, 24, 31, 38, … is 178? (a) 25th (b) 24th (c) 26th (d) 23rd
37. 37.Which term of the AP 1, 10, 19, 28, … is 127? (a) 15th (b) 16th (c) 17th (d) 14th
38. 38.What is the sum of all the whole numbers from 1 to 83? (a) 3403 (b) 3486 (c) 3487 (d) 6972
39. 39.What is the 16th term of the AP 18, 21, 24, 27, …? (a) 45 (b) 48 (c) 66 (d) 63
40. 40.Which term of the AP 9, 14, 19, 24, … is 164? (a) 31st (b) 34th (c) 33rd (d) 32nd

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