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Related to arithmetic progression: geometric progression, harmonic progression


(prŏ-gresh′ŏn) [L. progressus, going forward]
1. An advance or movement forward.
2. A worsening of a disease, e.g., of a cancer.
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Patient discussion about progression

Q. Is there a way stopping caries progress? I'm 17 and I've recently noticed I have chalky white spots on the back of two of my teeth at the bottom. I go to the dentist regularly (I have braces at the minute) and I'm assuming he's seen them but he hasn't mentioned them. I'm just curious as to weather caries are treatable? Is there anything my dentist can do to stop it progressing into something worse?

A. Caries starts by demineralization of the enamel. The enamel is the hardest material in our body. The bacteria gets the mineral out of it and it becomes weak. Start as white color and continues to a black unpleasant color as it progresses into the tooth. If you rinse your mouth often with fluoride and brush your teeth properly- it will stop the demineralization and the fluoride will take the place of other minerals in the enamel. This will stop the caries and the white spot will slowly becomes black. This is a good situation- it’ll be harder then before.

Q. My friend has Progressive MS, he is bound to a wheelchair, Prognosis? How can I help? He must be moved by a Hoyer Lift, he has caregivers. He has a beautiful voice and does have enough ability to move in his chair around local community. He has some bad days with spacicity, I want to help but am unsure as to how? He is 60? or so and lives on his own, he has had MS for many years and a number of complications, such as pneumonia and decubitus. Please help me to help him!

A. There are a number of ideas and resources for social and recreational activities (i.e. wheelchair sports, dancing, travel, aviation, etc.) that may be helpful, which can be found at

Q. Having chronic headaches, start in base of neck and progresses to migraine, worse when lying on stomach. Why? I have been having chronic headaches for the past 2 weeks. They start in the base of my neck and become migraines. They intensify when I lay on my stomach, blood rushes and they throb. Sometimes I can give myself relief by pressing firmly on my head or keeping my neck in a certain position. Just wondering if anyone knows what might be causing them.

A. Pinched nerve, bad posture is my problem anyway. I have a pinched nerve in my neck and my posture is horrible which causes me to get the worst headaches and they always start at the base of the neck and I always thought I had great posture (set up straight and all), but I was soooo wrong. Check with a Doctor and seek help from a Chiropractor if possible. They can do wonders. But for now, try lying on your back with a pillow or towel rolled up and placed under your neck only. It will support your neck and give it a nice crack too that helps a good deal too. That also helps keep the headaches away. Do you get sick to your stomach when the headaches come on?

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References in periodicals archive ?
--the maximum and minimum values show the same tendency of increasing the value of the arithmetic progression. The minimum value is equal as far as results are concerned for the fifth and the sixth grades;
Conversely, if [([T.sup.*n][T.sup.n]).sub.n [greater than or equal to] 0] is an arithmetic progression of strict order m-1, then (10) and (11) hold.
Thus we conclude that whenever both the first column and the first row are arithmetic progressions (2), the "fixed" sum
Now, Dubner and Nelson are thinking about taking the next step: going to eight consecutive primes in arithmetic progression. Dubner estimates that it would take about 20 times longer--at least 2.5 computer-years--to accomplish this search on his souped-up personal computers.
Therefore the new sequence {[M.sub.(k,t)]} generated from {[a.sub.n]} is an arithmetic progression with
Thus the arithmetic progression T(k) + 1 + kT(k)t has initial term coprime to its increment and by Dirichlet's Theorem contains infinitely many primes.
Looking in turn at elementary methods, complex analysis methods, and probabilistic methods, he considers such topics as prime numbers, arithmetic functions, sieve methods, the method of van der Corput, the Euler gamma function, summation formulae, the prime number theorem and the Riemann hypothesis, two arithmetic application, primes in arithmetic progressions, densities, distributions of additive functions and mean values of multiplicative functions, and integers free of small prime factors.
Among the topics examined are the distribution of primes (long arithmetic progressions of primes and small gaps between primes), class groups of binary quadratic forms, various aspects of the theory of L-functions, the theory of modular forms, and the study of rational and integral solutions to polynomial equations in several variables.
For centuries, mathematicians have wondered how many arithmetic progressions such as these exist among the set of prime numbers and how long the progressions can get.
You could see if your students could discover that the number of fish for any value of C is C(C+1)/2, a well-known formula from arithmetic progressions which your students will meet later on in their mathematics courses, and is the formula for triangular numbers.
Next they could investigate arithmetic progressions by typing 2 in A1, 5 in A2, and filling down for about 10 cells.