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  • If  is GP with general term <img alt="T_n=3.5^n" src="http://entrancecorner.oncodecogs.com/gif.latex?T_n%3D3

If G_1 is GP with general term T_n=3.5^n and  G_2 is GP with general term T_n=5.3^n. Then the ratio of third terms of GPs G_1G_2 and G_2 is

Option: 1

125


Option: 2

250


Option: 3

375


Option: 4

500


Answers (1)

best_answer

As we learnt

The general term or nth term of a geometric progression is a_n=ar^{n-1}

and

Properties of a GP

If a_{1},a_{2},a_{3},---------and \, b_{1},b_{2},b_{3} are 2 GPs, then the sequence

a_{1}b_{1},a_{2}b_{2},a_{3}b_{3},--------- is also a GP

-

 

 T_n \: \: for \: \: G_1G_2= 3.5^n\times 5.3^n= 15^{n+1}

T_n \: \: for \: \: G_2= 5.3^n

Ratio= \frac{3^{n+1}.5^{n+1}}{3^{n}.5}= 3.5^n= 3.5^3= 375

 

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