Question

Write the recursive formula for the geometric sequence.

a1 = -2  a2 = 8  a3 = -32

Answer 1

$a_1 = -2,\ a_2 = 8,\ a_3 = -32\\\\a_2=a_1\cdot(-4)\ \ \ and\ \ \ a_3=a_2\cdot(-4)\\\\ the\ recursive\ formula:\\\\ \left \{ {\big{a_1=-2\ \ \ \ \ \ \ \ \ \ \ } \atop \big{a_n=a_{n-1}\cdot(-4)}} \right.$

Answer 2

$a_1 = -2,\ \ a_2 = 8,\ \ a_3 = -32\\\\r=\frac{a_{2}}{a_{1}}=\frac{8}{-2}=-4 \\\\The \ recursive \ formula \ for \ a \ geometric \ sequence \ is \ written \ in \ the \ form:\\\\ a_n=a_{n-1} \cdot r\\ \\ a_n=a_{n-1} \cdot (-4 )$