Geometric progression

Fill 4 numbers between 4 and -12500 to form geometric progression.

Correct result:

a₁:  -20
a₂:  100
a₃:  -500
a₄:  2500

Solution:

$$\begin{gathered} q=-{\left(\mathrm{\mid }{\displaystyle \frac{-12500}{4}}\mathrm{\mid }\right)}^{{\displaystyle \frac{1}{4+1}}}=-5 \\ {a}_1=4\cdot (-5)=-20 \end{gathered}$$

$a_2=4\cdot (-5)\cdot (-5)=100$

$a_3=4\cdot (-5)\cdot (-5)\cdot (-5)=-500$

$a_4=4\cdot (-5)\cdot (-5)\cdot (-5)\cdot (-5)=2500$

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