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mathmath333
 one year ago
Fun question
mathmath333
 one year ago
Fun question

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1\(\large \color{black}{\begin{align}& \normalsize \text{Find the 20th term of the sequence }\hspace{.33em}\\~\\ &1,\ 5,\ 15,\ 34,\ 65\cdots\cdots \end{align}}\)

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.0do u really know how does the magic squares works ? it would be fun to play with

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.0oh so u just know the formula that defines the suitable sum xD nvm

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1no i dont know any formula for this nth term

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.0:) lets see if someone else know

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it s 4010 and here is the formula a(n) = n*(n^2 + 1)/2.

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1there may be the predefined nth term , but thats not any fun doing this

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@mathmath333 what do you think ?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1i think we should do any observation

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so enjoy observing :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the first 20 term : 1, 5, 15, 34, 65, 111, 175, 260, 369, 505, 671, 870, 1105, 1379, 1695, 2056, 2465, 2925, 3439, 4010

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1how did u know the formula by the way

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.0will ok i have this idea , we have 5 terms , so lets set a polynomial of order 4 \(\Large x_n= an^4+bn^3+cn^2+dn+e \\ \Large x_0=1 ~~thus e=1 \\ \Large x_1=a+b+c+d+1=5 \\ \Large x_2=16a+8b+4c+2d+1=15 \\\Large x_3=81a+27b+9c+3d+1=34\\ \Large x_4= 256a+64b+16c+4d+1=65 \) so now we have 4 equations with 4 variables :)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1that looks little cumbersome

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you have to focus all the numbers and then doing some arbitrary tries to guess the formular . then you customize all the tries . and you get the right one . doing this is maybe innate or it needs a few of experience dealing with sequence

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.0well this is one way to do it . u can make sine cos combination (fourier)

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.0anyway this is wolfram answer for the new polynomial (as u dont wanna the predefined )

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ikram002p gave you the normal right method to follow when dealing with those kind of sequence

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1ok a hint \(\large \color{black}{\begin{align} &1,\\~\\&\ 2+3,\\~\\&\ 4+5+6,\\~\\&\ 7+8+9+10,\\~\\&\ 11+12+13+14+15 \\~\\&\cdots\cdots \\~\\ \end{align}}\)

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.0this is what been defined :O

dan815
 one year ago
Best ResponseYou've already chosen the best response.1they just seem so close to doubling lol

dan815
 one year ago
Best ResponseYou've already chosen the best response.1solve a,b,c and u will ahve an equation that can get any xth term T(x)=...

dan815
 one year ago
Best ResponseYou've already chosen the best response.1I dont personally like this method though, we havent probven its a diff of 3 from there :)

dan815
 one year ago
Best ResponseYou've already chosen the best response.1but then again the equation u get does saitsfy all the terms uare given, so u cannot say its wrong

dan815
 one year ago
Best ResponseYou've already chosen the best response.1but then again the argument is that, there is obviously going to be some polynomial equation taht will will any given finite sequence,

dan815
 one year ago
Best ResponseYou've already chosen the best response.1as long as the polynomial equation solved is a sufficiently lower degree than the sequence given, or actually as long as its 1 degree lower than the number of tgerms given, we can say this polynomial equation solves the whole sequence

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1ok i will give a last hint

dan815
 one year ago
Best ResponseYou've already chosen the best response.1WAIT !! i solve it, u want me to do it another way!! dont tell me

dan815
 one year ago
Best ResponseYou've already chosen the best response.11 5 15 34 65 . . . 1 2+3 4+5+6 7+8+9+10

dan815
 one year ago
Best ResponseYou've already chosen the best response.1oaky so all we gotta do is calculate the nth term we will see at 20

dan815
 one year ago
Best ResponseYou've already chosen the best response.1and terms are going up at n*(n+1) so

dan815
 one year ago
Best ResponseYou've already chosen the best response.1have to know the sum of squares formula basically

dan815
 one year ago
Best ResponseYou've already chosen the best response.1i think i have ot subtract sum of series from that

dan815
 one year ago
Best ResponseYou've already chosen the best response.1dont mind the scribbles before lol

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1u have done it partially correct

dan815
 one year ago
Best ResponseYou've already chosen the best response.1maybe its subtract ugh xD

dan815
 one year ago
Best ResponseYou've already chosen the best response.1subtracting works i think

dan815
 one year ago
Best ResponseYou've already chosen the best response.1lemme just make it into a program i cant keep reyping that

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1well that works now this one , m still confuzed on how u got that but its correct \(\large \color{black}{\begin{align} k=\dfrac{n^2(n+1)}{2}\dfrac{n(n1)}{2 }\hspace{.33em}\\~\\ \end{align}}\)

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay ill show u what i did its simple first i looked at this picture

dan815
 one year ago
Best ResponseYou've already chosen the best response.1we need to see the last term on the 20th line

dan815
 one year ago
Best ResponseYou've already chosen the best response.1and for every line we get 1 new term

dan815
 one year ago
Best ResponseYou've already chosen the best response.1so its the sum of increasing number by 1

dan815
 one year ago
Best ResponseYou've already chosen the best response.1um ya the main thing is to just find the nth term u are dealing with

dan815
 one year ago
Best ResponseYou've already chosen the best response.1to count the number of tertms, we see it has this form which is 1,2,3,4.... first term has 1 term,2nd term has 2 terms, 3rd term has 3 terms and so on... for 20th term we have 20 terms, and how many terms hae passed by till that time, that would be 1+2+3+4....+19

dan815
 one year ago
Best ResponseYou've already chosen the best response.1that is the number we are adding +1 +2+3... to +19

dan815
 one year ago
Best ResponseYou've already chosen the best response.1i feel like im failing at explaining this lol, it should be simple xD

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1the idea was to spot the triangular numbers at the last place that is similar to Dan815's idea \(\large \color{black}{\begin{align} \color{red}{1},\\~\\\ 2+\color{red}{3},\\~\\\ 4+5+\color{red}{6},\\~\\\ 7+8+9+\color{red}{10},\\~\\\ 11+12+13+14+\color{red}{15 }\\~\\\cdots\cdots \\~\\ \end{align}}\) and then the \(20th\) term would have 19 terms as the pattern shows so \(\large \color{black}{\begin{align} 191+192+\cdots+210 \\~\\ \end{align}}\) thats easy to add now

dan815
 one year ago
Best ResponseYou've already chosen the best response.1thats a pretty different method from me

dan815
 one year ago
Best ResponseYou've already chosen the best response.1i did not notice that triangular number pattern there :O cool :)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1i thought u did it that way

dan815
 one year ago
Best ResponseYou've already chosen the best response.1hehe no its a bit different

dan815
 one year ago
Best ResponseYou've already chosen the best response.1but its interting the triangular numbers came up anayway
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