Recent questions tagged relationship-between-ap-and-gm

If $\large\frac{a_{2}a_{3}}{a_{1}a_{4}}$ = $\large\frac{a_{2}+a_{3}}{a_{1}+a_{4}}$ = $3\;(\large\frac{a_{2}-a_{3}}{a_{1}-a_{4}})$, then, $a_{1}$, $a_{2}$, $a_{3}$, $a_{4}$ are in

asked Jan 24, 2014 by yamini.v

1 answer

If $(m+n)^{th}$, $(n+1)^{th}$, $(r+1)^{th}$ term of an AP are in GP and $m, n, r$ are in HP, then ratio of first term of AP to common difference is

asked Jan 24, 2014 by yamini.v

1 answer

If AM and GM of two numbers are in ratio $p : q$, then the ratio of two numbers is

asked Jan 23, 2014 by yamini.v

1 answer

If $\;a_{1},a_{2},\;....\;a_{n}$ are in HP then $\;\large\frac{a_{1}}{a_{2}+a_{3}+\;..\;+a_{n}}\;,\large\frac{a_{2}}{a_{1}+a_{3}+...+a_{n}}\;,\large\frac{a_{3}}{a_{1}+a_{2}+a_{4}+\;...\;+a_{n}}\;,.....\;\large\frac{a_{n}}{a_{1}+a_{2}+....+a_{n-1}}\;$ are in

asked Jan 22, 2014 by yamini.v

1 answer

If a , b , c are in AP and A.G are arithmetic and geometric mean , between a and b while $\;A^{|}\;and\;G^{|}$ are A.M and G.M between B and C . then

asked Jan 22, 2014 by yamini.v

1 answer

If $a , b , c$ are three numbers in GP . and $\;a+x\;,b+x\;,c+x\;$ are in HP then $x$ equals

asked Jan 22, 2014 by yamini.v

1 answer

For $\;n \in N \;n \geq 25$ , Let A.G.H be A.M ,G.M and H.M of 25 and n . what is the least value of n such that A.G.H are all natural numbers greater than 25 .

asked Jan 22, 2014 by yamini.v

1 answer

If a,b,c are real and $\;4a^2+9b^2+16c^2-6ab-12bc-8ac=0\;$ the a,b,c are in

asked Jan 22, 2014 by yamini.v

1 answer

If $\;px^2+\large\frac{q}{x}\;\geq\;r\;$ for every +ve x $\;(p>0 , q>0)\;,\;$ then $\;27pq^2\;$ can not be less than

asked Jan 22, 2014 by yamini.v

1 answer

$p, q, r$ are three unequal numbers in AP. If $q-p$, $r-q$ and $p$ are in GP, the $p\;:\;q\;:\;r$ equals

asked Jan 21, 2014 by yamini.v

1 answer

If $j,k,l$ are in AP $p,q,r$ in HP and $jp,kq,lr$ in $GP$ , then $\;\frac{p}{r}+\frac{r}{p}\;is\;equal\;to:$

asked Jan 21, 2014 by yamini.v

1 answer

Let $\;a_{r}=\int\limits_{0}^{\frac{\pi}{4}}\;tan^{r}\;x\;dx$ , then $\;a_{1}+a_{3}\;,a_{2}+a_{4}\;,a_{3}+a_{5}\;$ are in

asked Jan 21, 2014 by yamini.v

1 answer

If $a_{1},a_{2},...a_{n}$ are in HP. , Then $\;a_{1}a_{2}+a_{2}a_{3}+.....+a_{n}\;a_{n-1}$ is equal to

asked Jan 20, 2014 by yamini.v

1 answer

If $a, b, c$ are in AP and $a^2$, $b^2$, $c^2$ in GP, and $a+b+c=\frac{3}{2}$, then value of $c$ is

asked Jan 20, 2014 by yamini.v

1 answer

If a, g and h are the AM, GM and HM respectively of two positive numbers x and y, then identify the correct statement.

asked Jan 18, 2014 by yamini.v

1 answer

If three numbers are in GP, then their logarithms will be in

asked Jan 17, 2014 by yamini.v

1 answer

The sum of three decreasing numbers in AP is 27. If -1, -1, and 3 are added to them respectively the resulting series is in GP. The numbers are

asked Jan 17, 2014 by yamini.v

1 answer

If arithmetic, geometric and harmonic means between two positive real numbers is A, G and H respectively, then, which of the following is true?

asked Jan 17, 2014 by yamini.v

1 answer

Given $4$ numbers, the first $3$ numbers are in $AP$ and the last $3$ numbers are in $GP$. The $1^{st}$ and $3^{rd}$ terms add upto $2$ and the $2^{nd}$ and $4^{th}$ terms add to $17$. Find the numbers.

asked Jan 6, 2014 by yamini.v

1 answer

If $a, b, c$ are in $AP, a, x, b$ and $b, y, c$ in $GP$, what is the progression type for $x^2,b^2,y^2$?

asked Jan 6, 2014 by yamini.v

1 answer

The product of $3$ numbers in $GP$ is $1000$. If $6$ and $7$ are added to the $2^{nd}$ and $3^{rd}$ terms respectively, the terms form an $AP.$ Find the $GP$.

asked Jan 3, 2014 by yamini.v

1 answer

How many terms of the series $6, 3, \large\frac{3}{2}$------ will make a sum of $\large\frac{765}{64}$.

asked Jan 2, 2014 by yamini.v

1 answer

How many terms of the series $\sqrt2$, 2, $2\sqrt2$,------- will make a sum of $62+31\sqrt2$ ?

asked Jan 2, 2014 by yamini.v

1 answer

What is the harmonic mean of the two roots of the following equation $(5+\sqrt2)x^2-(4+\sqrt5)x+8+2\sqrt5=0$

asked Jan 2, 2014 by yamini.v

1 answer

In an AP of 10 numbers and a HP of 10 numbers, the first term and last term are the same and equal to 2 and 3. Find the value of product of fourth term of the AP and the seventh term of the HP.

asked Jan 2, 2014 by yamini.v

1 answer

If the p and q are roots of the equation $x^2-7x+A=0\;\xi\;r\;\xi\;s$ are roots of equation $x^2-19x+B=0,$ find the values of $A\;\xi\;B$ if p,q,r,s are in AP.

asked Jan 2, 2014 by yamini.v

1 answer

If $a, b, c$ are in $AP$ and $a^2,b^2,c^2$ are in $HP$, how are $a, b$ and $\large\frac{-c}{2}$ related?

asked Jan 2, 2014 by yamini.v

1 answer

If the $ i^{th},j^{th}\; and\; k^{th} $ term of an AP and a GP are equal and are $x,y,z$ find the value of $x^{(y-z)}\;.y^{(z-x)}\;.z^{(x-y)}$

asked Jan 2, 2014 by yamini.v

1 answer

If a$\xi\;b$ are two positive integers,x is their AM and $y\;\xi\;z$ are two GMs then calculate the value of $\frac{y^3+z^3}{xyz}$

asked Jan 2, 2014 by yamini.v

1 answer

If the harmonic mean H and geometric mean G of two positive numbers a and b are in ratio 3:5, then a and b are in the ratio

asked Jan 2, 2014 by yamini.v

1 answer

An infinite GP has its first term as x and sum is 6 , then which of the following is true?

asked Jan 2, 2014 by yamini.v

1 answer

Given that four positive numbers are in HP, which of the following is true.

asked Dec 30, 2013 by yamini.v

1 answer

Among 5 numbers a, b, c, d and e the relationships are: a, b, c are in AP and b, c, d are in GP and c, d, e are in HP. Find b, c, d if a = 2 and e = 18.

asked Dec 30, 2013 by yamini.v

2 answers

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