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Chapter 6: Arithmetic Progressions

    Introduction

    Arithmetic Progressions

    nth Term of an Arithmetic Progression

    Sum of First n Terms in AP

    Geometric Progression

    nth term of a Geometric Progression

    Summary

    Enhanced Curriculum Support

    Easy Level Worksheet

    Moderate Level Worksheet

    Hard Level Worksheet

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Chapter 6: Arithmetic Progressions > Moderate Level Worksheet

Moderate Level Worksheet

Very Short Answer Questions (1 Mark Each)

(1) Find the 15th term of the A.P. 6, 11, 16, ….

Perfect! The 15th term is 76.

(2) Write the sum of the first n terms of an A.P. in terms of first and last terms.

Sn =

Correct! Where a is first term and l is last term.

(3) If the 1st term of an A.P. is 3 and 10th term is 48, find the common difference.

d =

Excellent! The common difference is 5.

(4) What is the last term of the A.P. 5, 10, 15, …, 50?

The last term given is:

Correct! The sequence ends at 50.

Short Answer Questions (2 Marks Each)

Note: Answer each question with steps and explanation, in 2-3 sentences. Write down the answers on sheet and submit to the school subject teacher.

(1) The 5th term of an A.P. is 22 and the 8th term is 34. Find the first term and common difference.

a = and d =

Perfect! First term = 6, common difference = 4.

(2) Find the sum of the first 20 terms of the A.P. 7, 10, 13, ….

S20 =

Excellent calculation! The sum is 710.

(3) How many terms are there in the A.P. 12, 17, 22, …, 82?

n =

Perfect! There are 15 terms in the sequence.

(4) Which term of the A.P. 100, 97, 94, … is the first negative term?

First negative term in the AP is term number:

Excellent! The 35th term will be the first negative term.

Long Answer Questions (4 Marks Each)

Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.

(1) The 8th term of an A.P. is 31 and the 15th term is 66. Find the first term and the sum of the first 20 terms.

d = and a = and S20 =

Excellent! First term = -4, Sum = 870.

(2) If the sum of the first n terms of an A.P. is 3n2 + 5n, find the A.P.

a1 = a2 = and d =

The A.P. is: , , , , ...

Perfect! The A.P. is 8, 14, 20, 26, ... with a = 8, d = 6.

(3) The sum of three numbers in A.P. is 21 and the sum of their squares is 165. Find the numbers.

The numbers are: , , (or) , ,

Excellent! The numbers are either 4, 7, 10 or 10, 7, 4.

Part B: Objective Questions (1 Mark Each)

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

(1) The 12th term of the A.P. 3, 7, 11, … is:

(a) 43 (b) 45 (c) 47 (d) 49

43
45
47
49

Correct! a12 = 3 + (12-1) × 4 = 3 + 44 = 47.

(2) If the 1st term of an A.P. is 6 and the 6th term is 21, the common difference is:

(a) 3 (b) 4 (c) 5 (d) 6

3
4
5
6

Correct! a6 = a + 5d, so 21 = 6 + 5d, giving d = 3.

(3) Which of the following represents the sum of the first n terms of an A.P. with a = 2, d = 3?

(a) Sn = n25n−1 (b) Sn = n24n+1 (c) Sn = n24n−1 (d) Sn = n23n+1

Sₙ = n/2(5n - 1)
Sₙ = n/2(4n + 1)
Sₙ = n/2(4n - 1)
Sₙ = n/2(3n + 1)

Yes! The sum for the given AP will be represented by the formula: Sn = n23n+1

(4) The 20th term of the A.P. 1, 4, 7, … is:

(a) 55 (b) 57 (c) 59 (d) 58

55
57
59
58

The 20th term for the AP will be 58!!

(5) In an A.P., the 1st term is 12 and 5th term is 0. The common difference is:

(a) -2 (b) -3 (c) -4 (d) -5

-2
-3
-4
-5

Correct! a5 = a + 4d, so 0 = 12 + 4d, giving d = -3.

(6) The last term of the A.P. 8, 14, 20, …, if it has 10 terms, is:

(a) 60 (b) 62 (c) 64 (d) 66

60
62
64
66

Correct! a10 = 8 + (10-1)×6 = 8 + 54 = 62.

(7) Which term of the A.P. 4, 7, 10, … is 94?

(a) 30th (b) 31st (c) 32nd (d) 33rd

30th
31st
32nd
33rd

Correct! 94 = 4 + (n-1)×3, so 90 = 3(n-1), giving n-1 = 30, so n = 31.

(8) The sum of the first 10 terms of the A.P. 5, 10, 15, … is:

(a) 200 (b) 250 (c) 275 (d) 300

200
250
275
300

Correct! S10 = 10225+95 = 510+45 = 5 × 55 = 275.

(9) In an A.P., the common difference is 0. Then the sequence is:

(a) Constant (b) Increasing (c) Decreasing (d) Cannot be determined

Constant
Increasing
Decreasing
Cannot be determined

Correct! If d = 0, all terms are equal, so the sequence is constant.

(10) If a = 1, d = 2, then the sum of first 50 terms is:

(a) 2450 (b) 2500 (c) 2600 (d) 2750

2450
2500
2600
2750

The sum of the first 50 terms is 2500!
3, 6, 9, 12, 15
-5, -1, 3, 7, 11
2, 4, 8, 16, 32
1, 1, 2, 3, 5
First term: a = 2, last term: l = 20
7, 7, 7, 7, 7
4, 6, 9, 13, 18
Arithmetic Progression
Not an A.P.
Cannot be determined

Arithmetic Progressions Challenge

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

The sum of an A.P. is always positive
Every sequence with equal differences is finite
In an A.P., the difference between consecutive terms is constant
The sum of first n natural numbers is n(n+1)/2
An A.P. can have both positive and negative common difference simultaneously
If three numbers a, b, c are in A.P., then 2b = a + c

Arithmetic Progressions Quiz