# 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} = a_{1} + (n-1)· d

In the example: a_{n} = 3 + (n-1)· 2 = 2n + 1

**Exercises**:

1.-Find out a_{n} and a_{10} of these progressions:

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

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

d) a_{1} = 3, a_{5} = 43

e) a_{7} = 15, a_{9} = 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, a_{10} = 39; b) a_{n} = 14 - 2n, a_{10} = -6; c) a_{n} = (3-n)/2= -n/2+3/2, a_{10} = -7/2; d) a_{n} = 10n - 7, a_{10} = 93; e) a_{n} = 5n - 20, a_{10} = 30

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

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