If a, b, c are in A.P.,b, c, d are in G.P.,an | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given that $a, b, c$ are in $A.P.$,we have $2b = a + c$ ..... $(i)$Given that $b, c, d$ are in $G.P.$,we have $c^2 = bd$ ..... $(ii)$Given that $c

Vedclass · Accepted Answer

$G.P.$

Vedclass · Answer

(C) Given that $a, b, c$ are in $A.P.$,we have $2b = a + c$ ..... $(i)$Given that $b, c, d$ are in $G.P.$,we have $c^2 = bd$ ..... $(ii)$Given that $c, d, e$ are in $H.P.$,we have $d = \frac{2ce}{c + e}$ ..... $(iii)$From $(ii)$,substitute $b = \frac{a + c}{2}$ and $d = \frac{2ce}{c + e}$:$c^2 = \left(\frac{a + c}{2}ight) \left(\frac{2ce}{c + e}ight)$$c^2 = \frac{(a + c)ce}{c + e}$$c^2(c + e) = (a + c)ce$$c^3 + c^2e = ace + c^2e$$c^3 = ace$Since $c 
eq 0$,we divide by $c$ to get $c^2 = ae$.Therefore,$a, c, e$ are in $G.P.$

If $a, b, c$ are in $A.P.$,$b, c, d$ are in $G.P.$,and $c, d, e$ are in $H.P.$,then $a, c, e$ are in

Similar Questions

If $a, b, c$ are in $A.P.$ and $a^2, b^2, c^2$ are in $G.P.$ such that $a < b < c$ and $a+b+c = \frac{3}{4}$,then the value of $a$ is

The difference between two numbers is $48$ and the difference between their arithmetic mean and geometric mean is $18$. The larger of the two numbers is:

The Geometric Mean $(G.M.)$ and Harmonic Mean $(H.M.)$ of two numbers are $10$ and $8$ respectively. The numbers are:

If the Arithmetic Mean of $a$ and $b$ is $\frac{a^{n+1} + b^{n+1}}{a^n + b^n}$,then $n = \dots$

The product of $n$ positive numbers is $1$. The sum of these numbers cannot be less than what value?

Vedclass Test Series

Exam Paper Generator

Online Exam Module