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  • Need explanation for: In a geometric progression, if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49, and the sum of the first and the third term is 35. Then the first term of this geometric progression is :

  In a geometric progression, if the ratio of  the sum of first 5 terms to the sum of their reciprocals is 49, and the sum of the first and the third term is 35. Then the first term of this geometric progression is :

  • Option 1)

    7

  • Option 2)

    21

  • Option 3)

    28

  • Option 4)

    42

 

Answers (2)

best_answer

As we learnt in 

Common ratio of a GP (r) -

The ratio of two consecutive terms of a GP

- wherein

eg: in 2, 4, 8, 16, - - - - - - -

r = 2

and in 100, 10, 1, 1/10 - - - - - - -

r = 1/10

Let the G.P is G, Gr, Gr2.................

Given that \frac{G+Gr+Gr^{2}+Gr^{3}+Gr^{4}}{\frac{1}{G}+\frac{1}{Gr}+\frac{1}{Gr^{2}}+\frac{1}{Gr^{3}}+\frac{1}{Gr^{4}}}= 49

\therefore G^{2}\frac{\left ( 1+r+r^{2}+r^{3}+r^{4} \right )}{\left ( 1+r+r^{2}+r^{3}+r^{4} \right )}= 49

\therefore G^{2}r^{4}= 49

\therefore Gr^{2}= 7

\therefore 35-G=7

     G=28

 


Option 1)

7

This option in incorrect

Option 2)

21

This option in incorrect

Option 3)

28

This option in correct

Option 4)

42

This option in incorrect

Posted by

divya.saini

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