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  • If the 4th, 7th  and 10th terms of a G.P. be a, b, c respectively, then the relation between  a, b, c  is <div class='qna-opt

If the 4th, 7th  and 10th terms of a G.P. be a, b, c respectively, then the relation between  a, b, c  is 

Option: 1

\begin{array}{l}{b=\frac{a+c}{2}}\end{array}


Option: 2

\begin{array}{l} \\ {a^{2}=b c}\end{array}


Option: 3

\begin{array}{l} {b^{2}=a c}\end{array}


Option: 4

\begin{array}{l}\\ {c^{2}=a b}\end{array}


Answers (1)

best_answer

Important Properties of a GP

If a_1,a_2,a_3,.....,a_{n-1},a_n are in G.P. with common ratio r, then-            a_r=\sqrt{a_{r-k}\cdot a_{r+k}},\;\forall\;k,\;0\leq k\leq n-r

In this Question,

 a_7 =\sqrt{a_{7-3}\cdot a_{7+3}}

a_7^2 =a_{4}\cdot a_{10}

b2 = a.c

 

Alternative Solution:

\\\text{Let A is first term of G.P and r is common ratio of G.P. }\\ t_{4}=a=Ar^3\\ t_{7}=b=Ar^6\\ t_{10}=c=Ar^{9}\\ b^2=A^2r^{12}=ac\\

Posted by

Devendra Khairwa

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