To do so we need to analyze how the consecutive terms are related. Let's find the quotient between each pair of consecutive terms.
ccccc
a_2/a_1&=& -4/2 &=& -2 [1.2em]
a_3/a_2&=& 8/-4 &=& -2 [1.2em]
a_4/a_3&=& -16/8&=& -2 [1.2em]
... & & ... & & ...
a_n/a_(n-1) = -2
We can see above that the quotient between the consecutive terms equals -2. Therefore, to obtain the value of the term in the n^(th) position, we need to multiply the previous term by -2. With this information and knowing that the first term equals 2, we can write the recursive formula.
a_1=2 and a_n=-2a_(n-1)
