What is Arithmetic Progression

Introduction:

The sequence or progression is a group of numbers or letters arranged in an order. These terms are generally denoted as a₁, a₂, a₃, a₄...a_n. The suffix 1, 2, 3….n, demonstrates the location of the term. There are a number of types of progressions. Arithmetic and geometric progressions are one of the types of the sequences.

Arithmetic Progression:

Arithmetic progression is also called as arithmetic sequence, It is a sequence that begins with an initial term a, and then each term is found by adding the common difference d.

General Form of arithmetic progression is,

a, a + d, a + 2d, a + 3d + . . .

The recursive formula is,

a_n = aⁿ⁻¹ + d.

To write the explicit form of an arithmetic series, we use

a_n = a₁ + (n − 1) d.

Example for Arithmetic Progression:

For the sequence is −2, 1, 4, 7, 10, 13, 16. . . Write the n^th term formula and find 20^th term.

Solution: Here, the common difference is, d = 3. The n^th term formula is,

a_n = − 2 + (n − 1)3

=> a₂₅ = − 2 + (20 − 1)3

=> a₂₅ = − 2 + 19 × 3

=> a₂₅ = 55.