matematika



Arithmetic Progression

An arithmetic progression is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.
For example, the sequence 3, 5, 7, 9, 11,... is an arithmetic progression with common difference 2.

Arithmetic progression property:

a1 + an = a2 + an-1 = ... = ak+an-k+1

Formula for finding the n-th term is defined by:

an = 1/2(an-1 + an+1)

If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the n-th term of the sequence is given by

an = a1 + (n - 1)d, n = 1, 2, ...

The sum S of the first n numbers of an arithmeric progression is given by the formula:

S = 1/2(a1 + an)n, where a1 is the first term and an the last.

or

S = 1/2(2a1 + d(n-1))n

Arithmetic Progression Calculator

First term
Common difference
Number of terms(n=?)


Arithmetic Progression Problems

1) Is the row 1,11,21,31... an arithemtic progression?
Solution: Yes, it is an arithmetic progression. Its first term is 1 and the common differnece is 10.


2) Find the sum of the first 10 numbers of this arithmetic series: 1, 11, 21, 31...
Solution: we can use this formula S = 1/2(2a1 + d(n-1))n
S = 1/2(2.1 + 10(10-1))10 = 5(2 + 90) = 5.92 = 460


3) Try to proove that if the numbers 1/(c + b), 1/(c + a), 1/(a + b) form an arithmetic progression then the numbers a2, b2, c2 form an arithmetic progression too.

List of arithmetic progression problems.

More about progressions in the math forum

Forum registration
Progressions forum


Send us math lessons, lectures, tests to:

  Math Bookstore   Questions and Answers
Copyright © 2005-2013.