arithmetic - What are the formal names of operands and results for ...
A famous theorem by¹ Fermat is that four squares cannot form an arithmetic progression. (Three definitely can: $1^2 = 1$, $5^2 = 25$ and $7^2 = 49$ already give an example). It already has been dis...
Modular arithmetic utilizes this "wrapping around" idea, after you reached the greatest element comes the smallest. So modular arithmetic is a sort of a mindset. A binary operation is an operation which combines two elements, for example addition is a binary operation since it combines two elements.
- does the proof above make sure that $a_n$ is not arithmetic? a sequence cannot be arithmetic and geometric at the same time, right? 2) what about more complex expressions? like $b_n=ln (n)$? how do I quickly see if it is arithmetic or geometric sequence?
There's more to say about three-term arithmetic progressions of squares, but first a review of Pythagorean triples, which turn out to be closely related to, but better studied than, three-term arithmetic progressions of squares.
Is there a 3-term arithmetic progression (AP) of perfect squares such ...
How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression? For example here is the sum of $\cos$ series: $$\sum_ {k=0}^ {n-1}\cos (a+k \cdot d) =\frac {\sin (n \times \f...
The actual question on the quiz In an arithmetic series, the terms of the series are equally spread out. For example, in 1 + 5 + 9 + 13 + 17, consecutive terms are 4 apart. If the first term in an arithmetic series is 3, the last term is 136, and the sum is 1,390, what are the first 3 terms?