An arithmetic sequence is usually given by a formula in which the nth term, T(n), is given in terms of the first term, a, and the common difference, d:
t(n) = a + d*(n-1) where n= 1, 2, 3, etc
An alternative is to define it iteratively. Thus:
t1 = a
tn = tn-1 + d , where n = 2, 3, 4, etc
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The history of arithmetic progression started with Euler. Later is was refined by Dirichlet which led to his theory of arithmetic progression.
what do you mean by mathematical designs using arithmetic progression
Airthmetic Progression
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Arithmetic progression was invented and discovered by two different mathematicians and scientists. Their names were Harvey Dubner and Tony Forbes.