Arithmetic vs Geometic -- Essay
Mar. 2nd, 2004 07:44 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
remulaHere's my completed (kinda) essay for math. *grin* Read it; you might learn something. =P All formatted and everything so I can copy, paste and print in fourth period. ^_~ Oh, and if you have anything for me to add to the geometric section, I'd really appreciate it. =P
Arithmetic vs Geometric
There are two basic types of sequences. They are arithmetic sequences and geometric sequences.
The easiest sequence to spot is generally the arithmetic sequence. In this sequence, there is an addition or subtraction generator and a common difference. To get the formula of an arithmetic sequence, first one would need to determine the common difference. The common difference would be the difference from one sequence number to the next.
5, 8, 11, 14, ... -- The common difference of this sequence would be 3.
Once the common difference is found, it would then be multipled by the term or a variable representing the term, such as "x".
f(n) = 3n -- Where "n" represents the term.
Next, one would substitute in a term and its corresponding sequence number, such as the first term, 1 and 5.
5 = 3(1)
If the equation one has written is not true, such as the one written above, one must then find its generator, or the number which would be added or subtracted in the problem to make the equation true.
5 = 3(1) + x => 5 -3 = 3 -3 + x => 2 = x
Once one finds both the common difference and the generator, one must make sure the formula works for the entire sequence by substituting in another term in the formula.
f(n) = 3n + 2 => 8 = 3(2) + 2 => 8 = 6 + 2 => 8 = 8
The above statement is true which proves that the formula is correct for the sequence.
The generally harder sequence to spot is the geometric sequence. Geometric sequences have a multiplication or division generator. There is no formula to find the sequence formula. The easiest way to find the next term is by the common ratio or multiplier.
~Remula
Helen To
March 02, 2004
Algebra, Period 2
Essay
There are two basic types of sequences. They are arithmetic sequences and geometric sequences.
The easiest sequence to spot is generally the arithmetic sequence. In this sequence, there is an addition or subtraction generator and a common difference. To get the formula of an arithmetic sequence, first one would need to determine the common difference. The common difference would be the difference from one sequence number to the next.
Once the common difference is found, it would then be multipled by the term or a variable representing the term, such as "x".
Next, one would substitute in a term and its corresponding sequence number, such as the first term, 1 and 5.
If the equation one has written is not true, such as the one written above, one must then find its generator, or the number which would be added or subtracted in the problem to make the equation true.
Once one finds both the common difference and the generator, one must make sure the formula works for the entire sequence by substituting in another term in the formula.
The above statement is true which proves that the formula is correct for the sequence.
The generally harder sequence to spot is the geometric sequence. Geometric sequences have a multiplication or division generator. There is no formula to find the sequence formula. The easiest way to find the next term is by the common ratio or multiplier.
~Remula
