What are at least 2 real-life examples of a sequence or series?
361299
2, 9, 16, 23, 30\n\nU(n+1) = Un + 7\n\nMoving through weeks on a calendar.\n\n\n\n50, 100, 200, 400\n\nU(n+1) = 2Un\n\nDoubling ingredients in a recipe.
1173957
Huh?  Please, provide examples of what you are talking about so that we can respond.
203992
a) [1,2] is a sub set of domain of g so for every x in [1,2]\nwe have a unique value of g.\n\nb) if the sequence converge, in the limit Xn+1 must be equal to X, so if the limit is L we have:\n\nL=(3L^2+3)^1/4\n\nL^4=3L^2+3\n\nL^4-3L^2-3=0\n\ndelta=9+12=21\n\nL^2=(3+√21)/2  (L^2>0)\n\nL = √[(3+√21)/2]  (L>0 because X0>0)\n\n4<√21<5  ---> 7<3+√21<8\n\n---> 3<(3+√21)/2<4  ---> 1<L<2\n\nc) we have (Xn+1)^4=3Xn^2+3 let Yn be Xn^2\n\n---> (Yn+1)^2=3Yn+3 ---> Yn
967058
It depends on what you are wanting to prove. Generally speaking, when you substitute numbers, you are restricting to a specific example. You cannot prove a general result by only looking at specific examples (unless you somehow show those specific cases give *all* the possibilities). However, you *can* show a result is false, if it is false for some specific example, so to show a general result is false, it is enough to 'plug in numbers'.
381290
I have an iterative method that is good for at least 80% of these types of problems.\n\nFirst, write down the series.\n\nNext, above the line you just wrote, write the difference between each pair of elements. In this case, it will be 1, 2, 4, 8, .... In this case, the answer is obvious - they are powers of two. The next one in the differences line should be 16, so the next on the original line should be 15+16=31. This will allow you to get any member in the sequence.\n\nIf the first order of differences doesn't give rise to a discernable pattern, try the differences of differences and so on.
1186148
There used to be a lot of them, but with computers these days they are being solved by brute force. Examples include Fermat's Last Theorem and the Four Color problem in topology. You can look those up to see what they are, and you will probably find sites listing other unsolved mathematical puzzles.
844539
1. An arithmetic sequence has a(sub 5)= -10 and a(sub 12) =18. Find a(sub 2) and a(sub 17)\n\nLet a(sub 1) = a and d = common difference.\nFor an AP:\na(sub n) = a + (n - 1)d\n\nSo a(sub 5) = a + 4d = -10 .... (1)\nand a(sub12) = a + 11d = 18 . (2)\nEquation (2) - equuation (1)\n7d = 28\nSo d = 4\nSo a = -26\na(sub 2) = a + d = -22\na(sub 17) = a + 16d = 38\n\n2. Find s(sub 4) for the geomtric sequence: \na(sub 1) = 5p, a(sub 2) = -10p\n\nLet a(sub 1) = a and common ratio be r\n\nFor a GP\na(sub n) = ar^(n-1)\n\na(sub 1) = a = 5p .......... (1)\na(sub 2) = ar =  -10p ..... (2)\nEquation (2)/equation (1)\nr = -2\n\nSo a(sub n) = 5p * (-2)^(n-1)\n\ns(sub n) = a(r^n - 1)/(r - 1)\n= 5p((-2)^n) - 1)/(-2 - 1)\n= -5p/3 ((-2)^n - 1)\n\nSo s(sub 4) = -5p/3 ((-2)^4 - 1)\n= -25p
924398
practically everywhere:\nfibonaci numbers in nature for eg
378842
In brief, follow as many normal forms as possible in sequence. (possibly with an exception of 1NF)
580109
ans is 70\n(5*2+1) (11*2+2) (24*2+3)\nrule is there r two series 5 11 24 51...\n7 16 34 70\n(7*2+2) (16*2+2) (34*2+2)
976290
There are lots of them.  The story of Fibonacci numbers is interesting.  Also, some background on the Pythagoreans:\n\nhttp://en.wikipedia.org/wiki/Portal:Mathematics
815141
You can find a bunch of them in this website:\nhttp://www.mathpuzzle.com/
669748
Just think a bit to locate the pattern by lookinh the first four terms.\nYou either get a common fifference or common ratio, ie you get AP or GP.\n\nIf the series is in fraction and above two does not comes, take reciprocal and see for common diffrence, Harmonic Pogression.\n\nIn word problem you have to figure out the pattern first, then apply formula...hope it helps!
723065
The sequence is the given series is *2 *3 *4 *5 *6and so on...so the answer is 720
729616
Could you give a few examples please?
280123
no, not in general.  Example:  Z(2)+Z(2) and Z(4) all are of order 4 but are not issomorphic because the element 3 of Z(4) has order 4 but there does not exist an element of order 4 in Z(2)+Z(2).
163546
Exponential graphs appear EVERYWHERE in the real world. \n\nFor example, they are used in :\n\n1. radioactive dating\n2. acoustic analysis of theatres\n3. stock market management\n4. estimation of stellar magnitudes\n5. analysis of the pH of solutions\n6. analysis of earthquakes\n7. tuning pianos\n8. tempering musical scales\n\nand many many more places.