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Karon86
 one year ago
What is the 100th term of sequence:
1,3,6,10,15,....
Write a explicit formula
Karon86
 one year ago
What is the 100th term of sequence: 1,3,6,10,15,.... Write a explicit formula

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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443915861353:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1the jump from 1 to 3 is +2 dw:1443915905024:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1the jump from 3 to 6 is +3 dw:1443915932403:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1the jump from 6 to 10 is +4 dw:1443915954079:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1the jump from 10 to 15 is +5 dw:1443915976631:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so what you can do is keep this pattern up until you have generated 100 terms OR you can find an explicit closed formula so you can avoid using recursion (recursion is long and tedious for a lot of terms)

Karon86
 one year ago
Best ResponseYou've already chosen the best response.0I want an explicit formula

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I prefer the second method each difference (+2, +3, +4, +5, ...) is separated by 1 each time this second level of finite differences suggests we have a 2nd degree polynomial

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443916308731:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1the general quadratic is ax^2 + bx + c

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1plug in x = 1 and we get ax^2 + bx + c = a*1^2 + b*1 + c = 1a+1b+c = a+b+c the input is 1, and the output is 1 dw:1443916381381:dw so a+b+c = 1

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1next plug in x = 2 (circled) to get ax^2 + bx + c a*2^2 + b*2 + c 4a+2b+c this is equal to the output of 3 (circled) in the second row dw:1443916438115:dw so 4a+2b+c = 3

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1443916456906:dw plug in x = 3 ax^2 + bx + c a*3^2 + b*3 + c 9a+3b+c the output is 6, so 9a+3b+c = 6

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1we now have this system of equations a+b+c = 1 4a+2b+c = 3 9a+3b+c = 6

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1do you know how to solve for a,b,c?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you have a number of options 1) elimination 2) substitution 3) matrices

Karon86
 one year ago
Best ResponseYou've already chosen the best response.0Dude. Like, That is totally different from what I am taught by the book

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0i contend that it can be any value we want it to be if there are no other conditions for the sequence.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1@Karon86 how does the book show you? what method do they use?

Karon86
 one year ago
Best ResponseYou've already chosen the best response.0To find the explicit formal, expand the first few terms of the sequence(sorry I have a terrible iPad): A1: 1 A2: 1+2 = 3

Karon86
 one year ago
Best ResponseYou've already chosen the best response.0A3: 1+2+3 = 6 A4: 1+2+3+4=10

Karon86
 one year ago
Best ResponseYou've already chosen the best response.0A5:1+2+3+4+5=15 An: 1+2+...+n

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I see, let me think

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1can you find an explicit formula for An: 1+2+...+n

Karon86
 one year ago
Best ResponseYou've already chosen the best response.0I don't know, the book doesn't says: Therefore: An=1+2+3+...+(n2)+(n1)+n. (this is whatI I am so confused) Which you can write as An=n+(n1)+(n2)+....+3+2+1

Karon86
 one year ago
Best ResponseYou've already chosen the best response.0I am confused with what comes after therefore

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1notice how the n pairs with 1, n1 pairs with 2, n3 with 3, etc etc

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1if you were to add up those pairs you'd get n+1 = n+1 n1+2 = n+1 n2+3 = n+1 ... ... ... 3+n2 = n+1 2+n1 = n+1 1+n = n+1

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1this video might help make things click a bit better? https://www.youtube.com/watch?v=aaFrAFZATKU let me know if it doesn't

Karon86
 one year ago
Best ResponseYou've already chosen the best response.0I cannot acces the YouTube video because it won't let me on th iPad. Please forgive me. Could you tell me the name of the YouTube video

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1do you have access to a laptop or desktop computer?

Karon86
 one year ago
Best ResponseYou've already chosen the best response.0No sir but if I can acces it on my phone. God I wish I had a laptop of desktop
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