## anonymous 5 years ago If 16, x, 9 are the first 3 terms of a geometric sequence, find the exact value of x can someone tell me how to find it please :) thanks

1. anonymous

${16 \over x}={x \over 9}$

2. anonymous

$$x=12$$

3. anonymous

$$x=-12$$ is also a solution.

4. anonymous

16=4^2 9=3^2 x should be 3.5^2 = 12.25

5. anonymous

A geometric sequence is a sequence in which a term $$a_i$$ can be found by multiplying the previous term $$a_{i-1}$$ by some constant $$d$$. In our case d could be $$-3/4$$ or $$3/4$$.

6. anonymous

??? i got 3/4 too but thats wrong the right answer is 12 but i dont understand how they got it why did you put it in a fraction???

7. anonymous

Yeah x is either $$12$$ or $$-12$$. You get it by solving the equation I put in my first comment.

8. anonymous

In a geometric sequence, the quotient of any two consecutive in the sequence must give the same value. So, in our case, $$16/x =x/9$$. Solve this equation for x and you will get the answer.

9. anonymous

thank you :)

10. anonymous

You're welcome :)