Question

G.P Class 11


Q. Which term of the G.P √3 , 3 , 3√3 is 729 ?


Explain in steps tomorrow my exam plss

Answer 1

Heya !
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★Geometric Progressions ★
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→ √3 , 3 , 3√3 forms a G.P with


....first term a = √3

.....common ratio r = √3

.....nth term = 729


=> We have to find n = ?


★ We know that the nth term of G.P


$= ar {}^{n - 1}$

putting the values in formula ,

$= > ar {}^{n - 1} = 729 \\ \\ = > \sqrt{3} \times ( \sqrt{3} ) {}^{n - 1} = 729 \\ \\ = > ( \sqrt{3} ) {}^{n} = 729 \\ \\ = > ( \sqrt{3} ) {}^{n} = ( \sqrt{3} ) {}^{12}$

★Now since the bases are same , powers will be equal .


•°• n = 12 ✔
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Thus, 729 is the 12 th term of the G.P !!


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Answer 2

G.P = √3, 3 , 3√3 ......


Formula is ar^n-1


Here n = ? , a = √3 nd r also = √3


So , √3 × √3^n-1 = 729


√3^n = √3^12


Compare the powers n = 12

It is 12th term