Chat with our AI personalities
The question cannot be answered because it assumes something which is simply not true. There are some situations in which arithmetic progression is more appropriate and others in which geometric progression is more appropriate. Neither of them is "preferred".
In an arithmetic progression the difference between each term (except the first) and the one before is a constant. In a geometric progression, their ratio is a constant. That is, Arithmetic progression U(n) - U(n-1) = d, where d, the common difference, is a constant and n = 2, 3, 4, ... Equivalently, U(n) = U(n-1) + d = U(1) + (n-1)*d Geometric progression U(n) / U(n-1) = r, where r, the common ratio is a non-zero constant and n = 2, 3, 4, ... Equivalently, U(n) = U(n-1)*r = U(1)*r^(n-1).
Immediately springing to mind, geometric progression is used in accountancy in finding the Net Present Value of projects (specifically, the value of money each year based on the discount factor). It is also used in annuities, working out monthly repayments of loans and values of investments - compound interest is a geometric progression.
It is not possible to answer this question without information on whether the terms are of an arithmetic or geometric (or other) progression, and what the starting term is.
an arithmetic sequeunce does not have the sum to infinty, and a geometric sequence has.