Ask Me Help Desk - Sequence euation

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sequence euation

the givn is 3 -6 12 -24 find the sequence equation

what is the sequence equation of 3, -6, 12, -24

Each number is -2 times the previous. So you know it'll be something like

$A_n=c \cdot (-2)^n$ ,

where $A_n$ is the nth term and c is some constant that you have to figure out. It's simple enough to figure out what c is: just plug in the values for the first number.

$3=c \cdot (-2)^1$

$\frac{3}{-2^1}=c$

$c=-\frac{3}{2}$

So

$A_n=-\frac{3}{2} \cdot (-2)^n$

or to simplify a little more

$A_n=3 \cdot \frac{(-2)^n}{-2}$

$A_n=3 \cdot (-2)^{n-1}$

It is rather obvious that the numbers are multiples of 3.

Try $3\cdot (-2)^{n}, \;\ n=0,1,2......$

What's the next number?

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