Question

3. Factorise the numerator and divide them as directed

(i) x2 - 16 - X2 - 5x + 36 by - 4​

Answer 1

AnswEr:

$\begin{gathered}\begin{gathered}\frak{Given}\begin{cases} \sf{First\:Term\:(a)\:=\:17}\\ \sf{Last\:Term\:(L)\;=\; 350} \\ \sf{Common\: Difference\:(d)\:=\; 9}\end{cases}\end{gathered}\end{gathered}$

Given

FirstTerm(a)=17

LastTerm(L)=350

CommonDifference(d)=9

$\:\:\:\:\;\:\;\footnotesize\bold{\underline{\underline{\sf{\red{Formula\:For\:the\: Last\:Term\:is \:-}}}}}$

$\dag\;\:\large{\underline{\boxed{\sf{\purple{l\:=\; a +(n -1)d}}}}}$

$\large\bold{\underline{\sf \green{Putting\:Values-}}}$

$:\implies\sf \: 350 = 17 + (n -1)9::⟹350=$

$\implies\sf \:\cancel\dfrac{333}{9}$=

$:\implies\sf \: (n -1)$ = 37:⟹(n−1)=37:⟹(n−1)=37:⟹(n−1)=37

:

$\implies\sf \: n$ = 37 + 1:⟹n=37+1⟹n=37+1:⟹n=37+1

$:\implies\large\boxed{\sf{\purple{n\:=\;38}}}$

$\small\bold{\underline{\sf{\pink{Therefore\:Given\:AP\: Contains\: 38\:Terms.}}}}$

$\large\bold{\underline{\sf{Now\: Finding\: Sum -}}}$

$:\implies\sf \: S_{n}$ = \dfrac{n}{2} (a +l)::⟹S

$:\implies\sf \: S_{38}$ = $\dfrac{38}{2}(17 + 350):$⟹S

$:\implies\sf \: 19 \times 367::$⟹19×367:

$:\implies\large\boxed{\sf{\purple{6973}}}$

$\small\bold{\underline{\sf{\red{Sum \:of \: the \:Terms\: of \: the \: Given\: AP\; is \: 6973.}}}}$

${{2}^{2}^{3}^{4}^6}$