The sum of the 3rd and the 4th terms of a G.P. is 60 and the product of its first three terms is 1000. If the first term of this G.P. is positive, then its 7th term is :

 

  • Option 1)

    7290

  • Option 2)

    320

  • Option 3)

    640

  • Option 4)

    2430

 

Answers (1)

As we learnt in 

General term of a GP -

T_{n}= ar^{n-1}
 

- wherein

a\rightarrow first term

r\rightarrow common ratio

 

 Let first term is a andcommon ratio is r then

ar^{2}+ar^{3}=60

\therefore ar^{2}\left ( 1+r \right )=60 - - - -- - -\left ( i \right )

Also  a\times ar\times ar^{2}=1000

\therefore a^{3}r^{3}=1000

\left ( ar \right )^3=1000

ar=10

r=\frac{10}{a}

put r in \left ( i \right )

\frac{a\times 100}{a^{2}}\left ( 1+\frac{10}{a} \right )=60

\frac{5}{a}\left ( \frac{a+10}{a} \right )=3

\therefore 3a^{2}=5a+50

\therefore 3a^{2}-5a-50=0

3a^{2}-15a+10a-50=0

\therefore a=5, r=2

\therefore T_{7}=ar^{6}

=5\times 2^{6}=5\times 64=320


Option 1)

7290

Incorrect Option

Option 2)

320

correct Option

Option 3)

640

Incorrect Option

Option 4)

2430

Incorrect Option

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