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(-(1)/(4)\right)\cdot(-4)^n=(5)/(4)\cdot(-4)^n\\\\Answer:\boxed{a_n=-5\cdot(-4)^(n-1)\ other\ a_n=(5)/(4)\cdot(-4)^n}`