Arithmetic and Geometric Progressions

AP & GP Visualizer

Class 9–10 • Arithmetic & Geometric Progressions • Formulas with steps

AP terms GP terms Common d / r Highlighted term

Line graph of a_n vs term number n

Mode

Demo sequence

First term a

Common d

Terms n

Quick examples

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Terms separated by commas (need at least 3) 2, 5, 8, 11, 14

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Results

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Type—

First term a—

Common d / r—

Explicit formula—

Recursive formula—

Arithmetic Progression (AP)

Each term is obtained by adding a fixed number called the common difference (d).

a, a+d, a+2d, a+3d, …

n-th term: a_n = a + (n−1)d

Example: 2, 5, 8, 11 (d = 3). Equal vertical steps along the line.

Geometric Progression (GP)

Each term is obtained by multiplying by a fixed number called the common ratio (r).

a, ar, ar², ar³, …

n-th term: a_n = a · rⁿ⁻¹

Example: 3, 6, 12, 24 (r = 2). Points grow or shrink by the same factor along the line.

Step-by-step (Class 9–10)

1. Identifying AP or GP

1. Enter a series or choose a demo.

2. Common difference / ratio

1. Calculated after analysis.

3. Explicit formula (n-th term)

1. Calculated after analysis.

4. Recursive formula

1. Calculated after analysis.

NCERT Class 9–10 • Arithmetic Progression & Geometric Progression