Easy Level Worksheet

Very Short Answer Questions (1 Mark Each)

(1) Write the formula for the nth term of an arithmetic progression (A.P.). an=a+n−1dan=a+ndan=ndan=a−n−1d

(2) What is the common difference in the A.P. 7, 10, 13, 16, …?

Correct! Common difference d = 10 - 7 = 3.

(3) Find the 5th term of the A.P. 2, 4, 6, ….

Perfect! a₅ = 2 + (5-1)×2 = 2 + 8 = 10.

(4) What is the first term of the A.P. -5, -2, 1, 4, …?

Excellent! The first term a = -5.

Short Answer Questions (2 Marks Each)

(1) Find the 10th term of the A.P. 3, 8, 13, …. a10 =

Perfect! Here a = 3, d = 5, so a10 = 3 + (10-1)×5 = 3 + 45 = 48.

(2) If the first term of an A.P. is 4 and the common difference is 3, find the 12th term. a12 =

Excellent! a12 = 4 + (12-1)×3 = 4 + 33 = 37.

(3) Which term of the A.P. 5, 11, 17, … is 89? Term number =

Perfect! Using an = 5 + (n-1)×6 = 89, we get n = 15.

(4) Find the common difference of the A.P. if its 7th term is 22 and the 4th term is 13. d =

Excellent! Using a7 - a4 = (7-4)d, we get 22 - 13 = 3d, so d = 3.

Long Answer Questions (4 Marks Each)

(1) Find the 25th term of the A.P. 10, 7, 4, …. Also, find the sum of the first 25 terms. a25 = and S25 =

Perfect! a = 10, d = -3, so a25 = 10 + 24×(-3) = -62, and S25 = 2522×10+24×−3 = -650.

(2) In an A.P., the 3rd term is 7 and the 7th term is 15. Find the first term and the common difference. a = and d =

Excellent! From a3 = a + 2d = 7 and a7 = a + 6d = 15, solving gives a = 1 and d = 2.

(3) The 17th term of an A.P. is 85 and its common difference is 5. Find the first term and the sum of the first 20 terms. a = and S20 =

Perfect! From a17 = a + 16×5 = 85, we get a = 5. Then S20 = 2022×5+19×5 = 1050.

Part B: Objective Questions (1 Mark Each)

Choose the correct answer and write the option (a/b/c/d)

(1) The nth term of an A.P. is given by

(a) an = a + nd (b) an = a + (n - 1)d (c) an = a - (n - 1)d (d) an = nd

Correct! This is the standard formula for the nth term of an A.P.

(2) The common difference of the A.P. 15, 13, 11, 9, … is

(a) 2 (b) -2 (c) -4 (d) 4

Correct! d = 13 - 15 = -2. The sequence is decreasing.

(3) The 6th term of the A.P. 2, 4, 6, … is

(a) 10 (b) 12 (c) 14 (d) 16

Correct! a₆ = 2 + (6-1)×2 = 2 + 10 = 12.

(4) The sum of first n terms of an A.P. is given by

(a) Sn = n22a+d (b) Sn = n2a+l (c) Sn = n22a+n−1d (d) Sn = a + nd

Correct! This is the standard formula for the sum of first n terms of an A.P.

(5) The 10th term of the A.P. 1, 4, 7, … is

(a) 31 (b) 30 (c) 28 (d) 27

Correct! a10 = 1 + (10-1)×3 = 1 + 27 = 28.

(6) The common difference in the A.P. where a = 2, a2 = 5 is

(a) 1 (b) 2 (c) 3 (d) 4

Correct! d = a2 - a = 5 - 2 = 3.

(7) If the first term of an A.P. is 5 and common difference is 3, the 4th term is

(a) 11 (b) 12 (c) 13 (d) 14

Correct! a4 = 5 + (4-1)×3 = 5 + 9 = 14.

(8) Which of the following is not an A.P.?

(a) 2, 4, 6, 8 (b) 1, 3, 5, 7 (c) 3, 6, 12, 24 (d) -1, -3, -5, -7

Correct! 3, 6, 12, 24 is a geometric progression (ratio = 2), not arithmetic.

(9) In an A.P., if the 1st term is 7 and the common difference is -2, what is the 6th term?

(a) -3 (b) -5 (c) -7 (d) -9

Correct! a₆ = 7 + (6-1)×(-2) = 7 - 10 = -3.

(10) The number of terms in the A.P. 4, 7, 10, …, 31 is

(a) 10 (b) 9 (c) 8 (d) 7

Correct! Using 31 = 4 + (n-1)×3, we get n = 10.

Arithmetic Progressions Challenge

Determine whether these statements about A.P.s are True or False:

Arithmetic Progressions Quiz