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 $a_1, a_2, \dots, a_n$ are positive real numbers such that $a_1 \cdot a_2 \cdot \dots \cdot a_n = 1$,then their sum is:

The common difference of an $A.P.$ whose first term is unity and whose second,tenth and thirty-fourth terms are in $G.P.$ is

If the arithmetic mean of two positive numbers is $A$,their geometric mean is $G$,and their harmonic mean is $H$,then $H$ is equal to:

If $x, y, z$ are in Arithmetic Progression $(AP)$ and $x, y, t$ are in Geometric Progression $(GP)$,then in which progression are $x, x - y, t - z$?

The first term of an arithmetic progression is $1$. If the second,tenth,and thirty-fourth terms form a geometric progression,then the common difference of the arithmetic progression is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module