Names of sequence progressions.

Thread starter Aeneas
Start date May 13, 2012
Tags

Sequence

AI Thread Summary

The discussion centers on the mathematical progression defined by Un+1 = KUn + d, exploring its classification. It is noted that this can be reformulated into a recognizable form related to geometric progressions. The conversation highlights the relationship between arithmetic and geometric progressions while seeking a specific name for the new progression type. The participants express gratitude for clarifying the mathematical transformation. The thread concludes without a definitive name for this progression but emphasizes its connection to existing types.

May 13, 2012

Aeneas

If U_n+1=U_n + d defines an arithmetic progression, and U_n+1 = kU_n defines a geometric progression, is there a name for a progression defined by U_n+1 =KU_n + d? Thanks.

Mathematics news on Phys.org

May 13, 2012

tiny-tim

Science Advisor

Homework Helper

Hi Aeneas!

We can rewrite that as U_n+1 - d/(1 - K) =K(U_n - d/(1 - k)) …

geometric.

May 13, 2012

Aeneas

Many thanks tiny-tim!

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

View full post »

Thread 'Six Pencil Puzzle'

Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.

View full post »

Thread 'Imaginary Pythagoras'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...

View full post »