Geometric progression

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

Result

a1:  -20
a2:  100
a3:  -500
a4:  2500

Solution:

q=(125004)14+1=5  a1=4(5)=20q = - \left(|\dfrac{ -12500}4|\right)^\dfrac{1}{ 4+1} = -5 \ \\ \ \\ a_1 = 4\cdot (-5) = -20
a2=4(5)(5)=100a_2 = 4\cdot (-5)\cdot (-5) = 100
a3=4(5)(5)(5)=500a_3 = 4\cdot (-5)\cdot (-5)\cdot (-5) = -500
a4=4(5)(5)(5)(5)=2500a_4 = 4\cdot (-5)\cdot (-5)\cdot (-5)\cdot (-5) = 2500



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