Arithmetic progressions

An arithmetic progression is such a sequence of numbers that the difference of any two successive members of the sequence is a constant. The constant is called difference of the progression.

Example: 3, 5, 7, 9, …. d = 2

General term: a_n = a₁ + (n-1)· d

In the example: a_n = 3 + (n-1)· 2 = 2n + 1

Exercises:

1.-Find out a_n and a₁₀ of these progressions:

a) 3, 7, 11, 15,...

b) 12, 10, 8, 6,...

d) a₁ = 3, a₅ = 43

e) a₇ = 15, a₉ = 25

2.- The distance between the first and eighth row from the stage of a theatre is 4,5 m and 9,75 m, respectively.

a) How long is the distance between every two rows?

b) How far from the stage is the 17th row?

Solutions: 1.- a) an = 4n - 1, a₁₀ = 39; b) a_n = 14 - 2n, a₁₀ = -6; c) a_n = (3-n)/2= -n/2+3/2, a₁₀ = -7/2; d) a_n = 10n - 7, a₁₀ = 93; e) a_n = 5n - 20, a₁₀ = 30

2.- a) 0,75 m; b) 16,5 m