# Whats the missing term in the geometric sequence 36, __, 4?

Nov 27, 2015

$x = 12$

#### Explanation:

Now let the Middle term be $x$

$36 , x , 4$

So the definition of a geometric series is

a, ar,ar^2 ....ar^(n-1
|_____|

$$    n terms


Now from this we can come to some results

1) ->36*r = x

This is because every step of the series is being multiplied by a common number $r$

2)-> x*r = 4

Now from $\otimes 1$

$\implies 36 \cdot r \cdot r = 4$

$\implies \cancel{4} \cdot 9 \cdot {r}^{2} = \cancel{4}$

$\implies {r}^{2} = \frac{1}{9} , r = \frac{1}{3}$

$36 \cdot \frac{1}{3} = x$

$\cancel{3} \cdot 12 \cdot \frac{1}{\cancel{3}} = x$

$\therefore x = 12$