a1,a2,a3,a4,a5 are the terms of a g.p. log3 a1 + log3 a2 +...+ log3 a5 =2 . log3 (a5/a3) = -2 Find these terms.

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a1 , a2 , a3 , a4 and a5 are terms of a GP. So each term is equal to the previus term in the series multiplied by a common ratio.

As log(3) a1 + log(3) a2 +...+ log(3) a5 =2,

=>log(3) a1*a2*a3*a4*a5* = 2

=> log(3) a1* a1*r* a1*...

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a1 , a2 , a3 , a4 and a5 are terms of a GP. So each term is equal to the previus term in the series multiplied by a common ratio.

As log(3) a1 + log(3) a2 +...+ log(3) a5 =2,

=>log(3) a1*a2*a3*a4*a5* = 2

=> log(3) a1* a1*r* a1* r^2*a1* r^3* a1* r^4 = 2

=> log(3) [a1^5 * r^10] = 2

=> a1^5 * r^10 = 3^2 = 9

Also, log(3) [a5/a3] = log(3) r^2 = -2

=> 2* log (3) r = -2

=> log(3) r = -1

=> r = 1/3

a1^5 * (1/3)^10 = 3^2

=> a1^5 = 3^12

=> a1 = 3^(12/5)

The terms of the GP are a1=3^(12/5) , a2=3^(7/5), a3=3^(2/5), a4=3^(-3/5) and a5=3^(-8/5)

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