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.
a 1 = − 2 , a 2 = 8 , a 3 = − 32 r = a 1 a 2 = − 2 8 = − 4 T h e rec u rs i v e f or m u l a f or a g eo m e t r i c se q u e n ce i s w r i tt e n in t h e f or m : a n = a n − 1 ⋅ r a n = a n − 1 ⋅ ( − 4 )
The recursive formula for the geometric sequence with first term -2 and common ratio -4 is given by: { a_1 = -2, a_n = a_{n-1} \cdot (-4) }. This means each term is obtained by multiplying the previous term by -4.
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