1. Which of the following lists forms an arithmetic progression?
(a) 2, 4, 8, 16, …
(b) 3, 3, 3, 3, …
(c) 1, –1, –3, –5, …
(d) Both (b) and (c)
2. In an AP, if the first term \(a = 5\) and common difference \(d = –2\), then the 7th term is
(a) –7 (b) –9 (c) 19 (d) –19
3. The 15th term of the AP 3, 8, 13, 18, … is
(a) 73 (b) 78 (c) 68 (d) 83
4. Which term of the AP 21, 18, 15, … is –81?
(a) 30th (b) 35th (c) 32nd (d) 34th
5. The sum of the first 10 terms of the AP 2, 7, 12, … is
(a) 230 (b) 245 (c) 215 (d) 250
6. If the 3rd term of an AP is 8 and the 7th term is 20, the common difference is
(a) 2 (b) 3 (c) 4 (d) 5
7. How many two-digit numbers are divisible by 3?
(a) 29 (b) 30 (c) 31 (d) 32
8. If \(S_n = \frac{n}{2}[2a + (n-1)d]\), then the 20th term of the AP whose first term is 10 and \(d = 5\) is
(a) 105 (b) 110 (c) 115 (d) 100
9. Assertion (A): The sequence 0.6, 1.7, 2.8, 3.9, … is an AP.
Reason (R): In an AP, the difference between any two consecutive terms is constant.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
10. Assertion (A): The 25th term of the AP with \(a = 8000\), \(d = 500\) is ₹20 000.
Reason (R): The nth term of an AP is given by \(a_n = a + (n-1)d\).
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
11. Write the first four terms of the AP when \(a = –2\), \(d = 0\).
12. For the AP 159, \(\frac{1}{3}\), … find the first term and the common difference.
13. Find \(d\) of the AP: –1.2, –3.2, –5.2, –7.2, …
14. Which of the following is an AP? If yes, write the next two terms: 4, 10, 16, 22, …
15. Find the common difference of the AP whose 10th term is 0 and 15th term is –15.
16. State whether 301 is a term of the AP 5, 11, 17, 23, … . Give reason.
17. Find the 31st term of an AP whose 11th term is 38 and 16th term is 73.
18. The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
19. How many three-digit numbers are divisible by 7?
20. Determine the AP whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
21. Find the 20th term from the last term of the AP 3, 8, 13, …, 253.
22. A manufacturer produces 600 TV sets in the third year and 700 sets in the seventh year. Assuming production increases uniformly, find:
(i) production in the first year,
(ii) production in the tenth year,
(iii) total production in the first seven years.
23. Subba Rao started work in 1995 at an annual salary of ₹5000 and received an increment of ₹200 each year. In which year did his income reach ₹7000? Also find the total salary received by him up to that year.
24. 200 logs are stacked with 20 logs in the bottom row, 19 in the next, and so on. In how many rows are the logs placed and how many logs are in the top row? Also find the total number of logs if the pattern continues till the top row has 1 log.
25. Case Study: Salary Increment
Reena joined a job with starting monthly salary ₹8000 and annual increment of ₹500. Her salary forms an AP.
(i) Write the first three terms of the AP.
(ii) Find her salary in the 15th year.
(iii) In which year will her salary become ₹15 000?
(iv) Find the total salary she receives in the first 10 years.
26. Case Study: Ladder Rungs
The lengths of rungs of a ladder decrease uniformly by 2 cm from bottom to top. The bottom rung is 45 cm long and there are 8 rungs.
(i) Write the AP formed by the lengths of the rungs.
(ii) Find the length of the topmost rung.
(iii) Find the total length of wood required for all rungs.
(iv) If the ladder had 12 rungs with the same common difference, what would be the length of the top rung?
1. (d)
2. (a)
3. (a)
4. (b)
5. (b)
6. (b)
7. (b)
8. (a)
9. (a)
10. (a)
11. –2, –2, –2, –2 (1 mark for correct d, 1 mark for listing terms)
12. a = 159, d = –\(\frac{2}{3}\) (correct identification – 2 marks)
13. d = –2 (1 mark for difference, 1 mark for verification)
14. Yes, AP with d = 6; next terms 28, 34 (1+1 marks)
15. d = –3 (correct use of nth term formula – 2 marks)
16. No, because 301 does not satisfy \(a_n = 5 + (n-1) \times 6\) for integer n (2 marks)
17. a = –2, d = 5; a31 = 148 (correct equations – 2 marks, answer – 1 mark)
18. d = 1 (use of a17 – a10 = 7 – 3 marks)
19. 128 numbers (first term 105, last 994; n = 128 – 3 marks)
20. AP: 4, 10, 16, 22, … (solve pair of equations – 3 marks)
21. a25 = 123 (find total terms first – 3 marks)
22. a = 550, d = 25; (i) 550 (ii) 775 (iii) 4375 (each part 1–2 marks with formula)
23. Year 2005; total salary up to 2005 = ₹1 68 000 (multi-step with formula – 5 marks)
24. 20 rows; top row = 1 log (use Sn = 200 – 5 marks)
25. (i) 8000, 8500, 9000 (1 mark)
(ii) ₹15 000 (1 mark)
(iii) 15th year (1 mark)
(iv) ₹1 22 500 (1 mark)
26. (i) 45, 43, …, 31 (1 mark)
(ii) 31 cm (1 mark)
(iii) 304 cm (1 mark)
(iv) 23 cm (1 mark)
All questions are answerable from the NCERT chapter text. Reviewed by GFIS faculty.