If a,b,c are in A.P. , then {3^a},{3^b},{3^c} shall be in

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8. Sequences and Series

normal

If $a,\;b,\;c$ are in $A.P.$, then ${3^a},\;{3^b},\;{3^c}$ shall be in

A

$A.P.$

B

$G.P.$

C

$H.P.$

D

None of these

Solution

(b) As given $2b = a + c$

$ \Rightarrow {3^{2b}} = {3^{a + c}}$

or ${({3^b})^2} = {3^a}.\;{3^c}\;$

$i.e.\;{3^a},\;{3^b},\;{3^c}$ are in $G.P.$

Note : Students should remember this question as a fact.

Standard 11

Mathematics

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