Formulate the recursive formula for the following geometric sequence.{-16, 4, -1, ...} Show all your work please:)

The recursive formula for given sequence is:[tex]a_n = -\frac{1}{4}a_{n-1}[/tex]Step-by-step explanation:Given sequence is:-16, 4, -1, ...First of all, we have to find the common ratio. common ratio is the ratio between two consecutive terms of a geometric sequenceHere[tex]a_1 = -16\\a_2 = 4\\a_3 = -1\\Now\\r = \frac{a_2}{a_1} = \frac{4}{-16} = -\frac{1}{4}\\r = \frac{a_3}{a_2} = \frac{-1}{4} = -\frac{1}{4}[/tex]The recursive of geometric sequence is:[tex]a_n = r * a_{n-1}[/tex]Putting the value of r[tex]a_n = -\frac{1}{4}a_{n-1}[/tex]Hence,The recursive formula for given sequence is:[tex]a_n = -\frac{1}{4}a_{n-1}[/tex]Keywords: Geometric sequence, Recursive formulaLearn more about geometric sequence at:brainly.com/question/11286417brainly.com/question/12884373#LearnwithBrainly