====== Ch 06: Sequences and Series ======
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  * If $\frac{1}{a}$, $\frac{1}{b}$ and $\frac{1}{c}$ are in $G.P$. Show that $r=\pm \sqrt{\frac{a}{c}}$  --- //BISE Gujranwala(2015),BISE Sargodha(2015), BISE Sargodha(2017),BISE Lahore(2017)//

  * With usual notation show that $AH=G^2$ ---// BISE Gujrawala(2015)//

  * Find $n$, so that $\frac{a^n+b^n}{a^{n-1}+b^{n-1}}$ maybe $A.M$ between $a$ and $b$.  --- //BISE Gujrawala(2015)//

  * If $y=1+\frac{x}{2}+\frac{x^4}{4}+...$ Show that $x=2(\frac{y-1}{y})$  --- //BISE Gujrawala(2017)//

  * Find the $9th$ term of harmonic sequence $\frac{1}{3}, \frac{1}{5}, \frac{1}{7},...$ --- //BISE Gujrawala(2017)//

  * If $a=-2$, $b=-6$, find $A.G$  --- //BISE Gujrawala(2017)//

  * If $\frac{1}{a}$, $\frac{1}{b}$, $\frac{1}{c}$ are in $A.P$ then show that common difference is $\frac{a-c}{2ac}$ --- //BISE Sargodha(2015)//

  * If $15$ and $8$ are two A.Ms between $a$ and $b$, find $a$ and $b$. --- //BISE Sargodha(2015)//

  * If $S_2,S_3,S_5$ are the sum of $2n,3n,5n$ terms of $A.P$. Show that $S_5=5(S_3-S_2)$ --- //BISE Sargodha(2015), BISE Sargodha(2017)//

  * The sum of $9$ terms of an $A.P$. is $171$ and its eight term is $31$. Find series. --- //BISE Sargodha(2015)//

  * Find three $A.Ms$ between $3$ and $11$ --- //BISE Sargodha(2016)//

  * How many terms of $-7+(-5)+(-3)+...$ amount to $65$ --- //BISE Sargodha(2016),FBISC(2016)//

  * If $a=2i$, $b=4i$ show that $AH=G^2$ --- //BISE Sargodha(2016)//

  * If $y=\frac{2}{3}x+\frac{4}{9}x^2+\frac{8}{27}x^3+...$ and $0<x<\frac{3}{2}$ then show that $x=\frac{3y}{2(1+y)}$ --- //BISE Sargodha(2016),FBISE(2016)//

  * Insert two $G.Ms$ between $2$ and $16$ --- //BISE Sargodha(2017)//

  * If $y=\frac{x}{2}+\frac{1}{4}x^2+\frac{1}{8}x^3+...$ and $0<x<2$, then prove that $x=\frac{2y}{1+y}$ --- //BISE Lahore(2017)//

  * Insert four harmonic means between $\frac{7}{3}$ and $\frac{7}{11}$ --- //FBISE(2017)//

  * Show that sum of $n$ $A.Ms$ between $a$ and $b$ is equal to $n$ times their $A.M$. --- //FBISE(2017)//


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{{tag>FSc FSc_Part1 Important_Questions_FSc_1}}