Question

If a b and c in a
re in G.p.
show that following terms are also in Gp​

Answer 1

Answer:

If a,b,c are in G.P., prove that the following are also in G.P.:

If a,b,c are in G.P., prove that the following are also in G.P.:a3,b3,c3

Given a,b,c are in GP

Given a,b,c are in GP⟹b2=ac  .......... as b is G.M. of a and c

Given a,b,c are in GP⟹b2=ac  .......... as b is G.M. of a and cCubing on both sides 

Given a,b,c are in GP⟹b2=ac  .......... as b is G.M. of a and cCubing on both sides b6=a3c3

Given a,b,c are in GP⟹b2=ac  .......... as b is G.M. of a and cCubing on both sides b6=a3c3⟹(b3)2=(a3)(c3) 

Given a,b,c are in GP⟹b2=ac  .......... as b is G.M. of a and cCubing on both sides b6=a3c3⟹(b3)2=(a3)(c3) ∴b3isG.M.ofa3andc3

Given a,b,c are in GP⟹b2=ac  .......... as b is G.M. of a and cCubing on both sides b6=a3c3⟹(b3)2=(a3)(c3) ∴b3isG.M.ofa3andc3⟹a3,b3,c3 are in GP.

Step-by-step explanation:

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