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Question Number 97694 by mr W last updated on 09/Jun/20

Commented by Rio Michael last updated on 09/Jun/20

please sir translate the last part for us who don′t know what −−−−means

pleasesirtranslatethelastpartforuswhodon′tknowwhat−−−−means

Commented by mr W last updated on 09/Jun/20

i think it is to find the general term a_n =?

ithinkitistofindthegeneralterman=?

Commented by prakash jain last updated on 09/Jun/20

a_(n+1) −3a_n =6n^2 −12n+2 a_(n+1) −3a_n =f(n) Linear non−homogeneous equation. homogeneous solution λ−3=0⇒a_n =c3^n Particular solution g(n) since it is linear g(n) will be similar to f(n) g(n)=bn^2 +cn+d b(n+1)^2 +c(n+1)+d−3(bn^2 +cn+d)= 6n^2 −12n+2 b−3b=6⇒b=−3 2b+c−3c=−12 −2c=−12−2b=−6⇒c=3 b+c+d−3d=2 −3+3−2d=2⇒d=−1 g(n)=−3n^2 +3n−1 general solution a(n)=c3^n −3n^2 +3n−1

an+1−3an=6n2−12n+2an+1−3an=f(n)Linearnon−homogeneousequation.homogeneoussolutionλ−3=0⇒an=c3nParticularsolutiong(n)sinceitislinearg(n)willbesimilartof(n)g(n)=bn2+cn+db(n+1)2+c(n+1)+d−3(bn2+cn+d)=6n2−12n+2b−3b=6⇒b=−32b+c−3c=−12−2c=−12−2b=−6⇒c=3b+c+d−3d=2−3+3−2d=2⇒d=−1g(n)=−3n2+3n−1generalsolutiona(n)=c3n−3n2+3n−1

Commented by john santu last updated on 11/Jun/20

for n=1 a_1 = c.3−3+3−1 3 = 3c−1 ⇒ c =(4/3) a_n = 4.3^(n−1) −3n^2 +3n−1

forn=1a1=c.3−3+3−13=3c−1⇒c=43an=4.3n−1−3n2+3n−1

Commented by mr W last updated on 09/Jun/20

thanks for solving!

thanksforsolving!

Commented by I want to learn more last updated on 10/Jun/20

sir, i think for n = 1, a_1 = 3 ??? not 1

sir,ithinkforn=1,a1=3???not1

Commented by mr W last updated on 10/Jun/20

yes, you are right.

yes,youareright.

Answered by mathmax by abdo last updated on 09/Jun/20

perhaps the Q is find a_n

perhapstheQisfindan

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