Ch 06: Sequences and Series

  • 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 $y=1+\frac{x}{2}+\frac{x^4}{4}+\ldots$ Show that $x=2(\frac{y-1}{y})$ — BISE Gujrawala(2017)
  • Find the $9th$ term of harmonic sequence $\frac{1}{3}, \frac{1}{5}, \frac{1}{7},\ldots$ — 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 $-7+(-5)+(-3)+\ldots$ amount to $65$ — BISE Sargodha(2016),FBISC(2016)
  • If $a=2i$, $b=4i$ show that $AH=G^2$ — BISE Sargodha(2016)
  • If $y=\frac{2}{3}x+\frac{4}{9}x^2+\frac{8}{27}x^3+\ldots$ 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 $y=\frac{x}{2}+\frac{1}{4}x^2+\frac{1}{8}x^3+\ldots$ 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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