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The sum of the 3^rd and the 4^th 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 7^th term is :

Option 1)
7290

Option 2)
320

Option 3)
640

Option 4)
2430

Answers (1)

best_answer

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

Posted by

prateek

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