Class 10 Mathematics Activity Book Solutions: Arithmetic Progressions and Coordinate Geometry

Solved activity workbook pages for Class 10 Mathematics covering patterns, arithmetic progressions, and coordinate geometry formulas. Includes determination of terms, common differences, sums of series, distance formula, midpoint formula, and centroid of triangles.

Maths
English
· 3 topics
Checked against the video on 18 Oct 2026

Made by AI from the YouTube video 10th Mathematics activity book (opens YouTube in a new tab) by Avinash Nandyal, then checked against it. All credit for the teaching goes to the creator. Tap a topic’s time to confirm a fact in the video.

Class 10 Mathematics Activity Book Solutions: Arithmetic Progressions and Coordinate Geometry

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0:00

Arithmetic Progression Patterns and Common Difference

Must knowAn arithmetic progression (AP) can be identified by finding a constant common difference between consecutive terms in a number sequence.
Triangle toothpicks pattern forms the sequence 3, 5, 7 where each subsequent figure adds 2 sticks, giving a common difference of 2.
The 4-sided/adjacent triangle pattern generates the sequence 6, 11, 16, 21, 26, 31, 36, 41, 46, 51 with a common difference of 5.
In the sequence 1, 4, 7, 10, 13, 16, 19, 22, the common difference between consecutive terms is 3.
In the sequence 2, 5, 8, 11, 14, 17, 20, 23, the common difference between consecutive terms is 3.
In the decreasing sequence 3, 1, -1, -3, -5, -7, -9, -11, the common difference between consecutive terms is -2.
In the sequence 8, 5.5, 3, 0.5, -2, -4.5, -7, the common difference between consecutive terms is -2.5.

0:14

General Term and Sum Formulas of Arithmetic Progressions

Must knowThe general nth term of an arithmetic progression is given by the formula a_n = a + (n - 1)d, where a is the first term and d is the common difference.
Must knowThe sum of the first n terms of an arithmetic progression is calculated using S_n = (n / 2) × [2a + (n - 1)d].
For the sequence 2, 5, 8 with a = 2 and d = 3, the 10th term calculation gives a_10 = 2 + (10 - 1) × 3 = 29.
For the sequence 2, 5, 8, the sum of 10 terms is S_10 = (10 / 2) × [2(2) + (10 - 1)3] = 5 × [4 + 27] = 155.
For the arithmetic sequence 4, 11, 18, 25 with a = 4 and d = 7, the 20th term is a_20 = 4 + (20 - 1)7 = 4 + 133 = 137.
For the sequence 4, 11, 18, 25, the sum of the first 20 terms is S_20 = (20 / 2) × [2(4) + (20 - 1)7] = 10 × [8 + 133] = 10 × 141 = 1410.

0:23

Coordinate Geometry: Distance, Midpoint, and Centroid

The distance between two points (x1, y1) and (x2, y2) is given by d = sqrt((x2 - x1)² + (y2 - y1)²).
The length of line segment BD with perpendicular sides of lengths 4 and 3 units is calculated as sqrt(4² + 3²) = sqrt(16 + 9) = sqrt(25) = 5 units.
Distance between points B(3, 4) and C(7, 2) is calculated as BC = sqrt((7 - 3)² + (2 - 4)²) = sqrt(16 + 4) = sqrt(20) = 4.5 units (approx).
Distance between origin A(0, 0) and C(7, 2) is CA = sqrt((7 - 0)² + (2 - 0)²) = sqrt(49 + 4) = sqrt(53) = 7.3 units (approx).
The midpoint coordinates P of a segment joining (x1, y1) and (x2, y2) are given by ((x1 + x2)/2, (y1 + y2)/2).
For points A(0, 0) and B(3, 4), the midpoint P is ((0 + 3)/2, (0 + 4)/2) = (1.5, 2).
Must knowThe centroid G(x, y) of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).
For vertices A(0, 0), B(3, 4), and C(7, 2), the centroid is G = ((0 + 3 + 7)/3, (0 + 4 + 2)/3) = (10/3, 6/3) = (3.33, 2).
Must knowThe centroid divides each median of a triangle internally in the ratio 2:1 (or 1:2 depending on the reference vertex/base).

Key terms

Arithmetic Progression: A sequence of numbers such that the difference between the consecutive terms is constant.
Common Difference (d): The fixed amount added to each term to get the subsequent term in an arithmetic progression.
Centroid: The point of intersection of the three medians of a triangle, dividing each median in a 2:1 ratio.
Midpoint: The point on a line segment dividing it into two equal segments.

Formulas

a_n = a + (n - 1)d: General nth term of an AP
S_n = (n / 2) × [2a + (n - 1)d]: Sum of the first n terms of an AP
d = sqrt((x2 - x1)² + (y2 - y1)²): Distance between two points in a Cartesian plane
((x1 + x2)/2, (y1 + y2)/2): Coordinates of the midpoint of a line segment
((x1 + x2 + x3)/3, (y1 + y2 + y3)/3): Coordinates of the centroid of a triangle

Quick revision

The nth term of an AP is given by a_n = a + (n - 1)d.
The sum of n terms of an AP is S_n = (n/2)[2a + (n - 1)d].
In the sequence 4, 11, 18, 25, the common difference d is 7.
The 20th term of the AP 4, 11, 18, 25 is 137.
The sum of the first 20 terms of 4, 11, 18, 25 is 1410.
The midpoint between (0, 0) and (3, 4) is (1.5, 2).
The centroid of a triangle with vertices (0,0), (3,4), and (7,2) is (10/3, 2).
The centroid of a triangle divides each median in the ratio 2:1.

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Class 10 Mathematics Activity Book Solutions: Arithmetic Progressions and Coordinate Geometry

Maths
English
· 3 topics
Checked against the video on 18 Oct 2026

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Class 10 Mathematics Activity Book Solutions: Arithmetic Progressions and Coordinate Geometry

Class 10 Mathematics Activity Book Solutions: Arithmetic Progressions and Coordinate Geometry

Arithmetic Progression Patterns and Common Difference

General Term and Sum Formulas of Arithmetic Progressions