Arithmetic Progression Calculator

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Common difference (d):

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First term (a₁):

Common difference (d):

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First term (a₁):

nth term (aₙ):

Position (n):

nth term (aₙ):

Common difference (d):

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About Arithmetic Progression

An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, ... is an arithmetic progression with a common difference of 2.

Formulas

General term (nth term): a_n = a₁ + (n - 1)d

Sum of n terms: S_n = n/2[2a₁ + (n - 1)d] = n/2[a₁ + a_n]

Common difference: d = (a_n - a₁) / (n - 1)

First term: a₁ = a_n - (n - 1)d

Number of terms: n = (a_n - a₁) / d + 1

Examples

Example 1: Find the 10th term of the arithmetic progression 2, 5, 8, 11, ...

First term (a₁) = 2, Common difference (d) = 3, n = 10

Using the formula: a_n = a₁ + (n - 1)d

a₁₀ = 2 + (10 - 1) × 3 = 2 + 9 × 3 = 2 + 27 = 29

Example 2: Find the sum of the first 15 terms of the AP: 3, 8, 13, 18, ...

First term (a₁) = 3, Common difference (d) = 5, n = 15

Using the formula: S_n = n/2[2a₁ + (n - 1)d]

S₁₅ = 15/2[2 × 3 + (15 - 1) × 5] = 15/2[6 + 14 × 5] = 15/2[6 + 70] = 15/2 × 76 = 570