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

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(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

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$G.P.$

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(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

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