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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.
they look like arithmetic and geometric patterns in math
i need mathematical approach to arithmetic progression and geometric progression.
=Mathematical Designs and patterns can be made using notions of Arithmetic progression and geometric progression. AP techniques can be applied in engineering which helps this field to a large extent....=
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".
Arithmetic progression and geometric progression are used in mathematical designs and patterns and also used in all engineering projects involving designs.
Its an arithmetic progression with a step of +4.
For an Arithmetic Progression, Sum = 15[a + 7d].{a = first term and d = common difference} For a Geometric Progression, Sum = a[1-r^15]/(r-1).{r = common ratio }.
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).
This is referred to as a geometric progression - as opposed to an arithmetic progression, where each new number is achieved via addition or subtraction.
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.
Geometric
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.
1.The Geometric mean is less then the arithmetic mean. GEOMETRIC MEAN < ARITHMETIC MEAN 2.