Let me clarify. I only have the arithmetic mean. I don't have the data from which it was determined.
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.
Sure. There are other applications of arithmetic, but algebra without arithmetic is impossible. A broad knowledge of arithmetic is essential for mastery of algebra.
Of course. Formulas are not encountered until the student progresses from arithmetic to algebra.
axioms or postulates
An axiom.
"Arithmetic mean" means the same as average. "Mean", without qualifiers, usually refers to the arithmetic mean. However, there are other types of "means", for example, the geometric mean.
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.
Sure. There are other applications of arithmetic, but algebra without arithmetic is impossible. A broad knowledge of arithmetic is essential for mastery of algebra.
Of course. Formulas are not encountered until the student progresses from arithmetic to algebra.
uh... yes without a working memory you would not know (remember) how to do arithmetic
Of course! People were doing real arithmetic long before the first computer!
Edith M. Joy has written: 'Arithmetic without a pencil' -- subject(s): Mental arithmetic
One way to find log values without a logarithm book is to use the properties of logarithms. If you have a base and an exponent equal to a number, you can rewrite it in logarithmic form. Another method is to use a calculator or online tool to compute the log value of a number.
sketch
axioms or postulates
The alphabet of every language can be used as a geometric tool. Without writing, geometry is nearly impossible.
An axiom.