Class 10 - Chapter 5: Arithmetic Progressions

Section A (1 Mark each)

Q1. The 10th term of the AP: 5, 8, 11, 14, ... is:

(a) 32 (b) 35 (c) 38 (d) 185

Q2. If $k, 2k-1$ and $2k+1$ are three consecutive terms of an AP, the value of $k$ is:

(a) 2 (b) 3 (c) -3 (d) 6

Q3. The sum of first $n$ odd natural numbers is:

(a) $2n-1$ (b) $2n+1$ (c) $n^2$ (d) $n^2-1$

Q4. Assertion (A): The sequence 2, 4, 8, 16, ... is not an Arithmetic Progression.
Reason (R): A sequence is an AP if 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.

Section B (2 Marks each)

Q5. Which term of the AP: 21, 18, 15, ... is -81?

Solve on white paper.

Q6. Find the AP whose 3rd term is 5 and 7th term is 9.

Solve on white paper.

Q7. How many two-digit numbers are divisible by 3?

Solve on white paper.

Section C (3 Marks each)

Q8. Find the sum of the first 22 terms of the AP: 8, 3, -2, ...

Solve on white paper.

Q9. The sum of 4th and 8th terms of an AP is 24 and the sum of 6th and 10th terms is 44. Find the first three terms of the AP.

Solve on white paper.

Section D (5 Marks)

Q10. The sum of the first $n$ terms of an AP is given by $S_n = 4n - n^2$. Find the first term, the sum of first two terms, the second term, and the $n$th term.

Solve on white paper.

Section E (4 Marks)

Q11. Case Study: TV Production

A manufacturer of TV sets produced 600 sets in the third year and 700 sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year.

(i) Find the production in the 1st year.

(ii) Find the production in the 10th year.

(iii) Find the total production in first 7 years.

Solve on white paper.