Question

Write the explicit formula for the geometric sequence. a1 = -5 a2 = 20 a3 = -80

Answer 1

$a_1 = -5;\ a_2 = 20;\ a_3 = -80 \\\\a_2:a_1=r\ and\ a_3:a_2=r\\\\r=20:(-5)=-4\ check\ r=-80:20=-4\\\\a_n=a_1r^{n-1}\to a_n=-5\cdot(-4)^{n-1}=-5\cdot(-4)^{-1}\cdot(-4)^n\\\\=-5\cdot\left(-\dfrac{1}{4}\right)\cdot(-4)^n=\dfrac{5}{4}\cdot(-4)^n\\\\Answer:\boxed{a_n=-5\cdot(-4)^{n-1}\ other\ a_n=\frac{5}{4}\cdot(-4)^n}$