In a G.P., 5^ th term is 27 and 8^ th term is 729. Find its 11^ t… - Vidyadip

MCQ

In a $G.P., 5^{th}$ term is $27$ and $8^{th}$ term is $729.$ Find its $11^{th}$ term.

A
$729$
B
$2187$
C
$6561$
✓
$19683$

✓

Answer

Correct option: D.

$19683$

Given, $a_5 = 27$ and $a_8 = 729.$
$\Rightarrow ar^4 = 27$ and $ar^7 = 729$
On dividing we get, $r^3 = 27$
$\Rightarrow r=3$
$\Rightarrow\text{a}=\frac{23}{(3^4)}=\frac{1}{3}$
$\Rightarrow\text{a}_{11}=\text{a}^{10}$
$=(\frac{1}{3})(3^{10})$
$=39$
$=19683$

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