Question

Please help me with my ALGEBRA! Picture included!

Answer 1

`\text{If a, b, c, d,... is an arithmetic sequence, then}\ b-a=c-b=d-c\\\\\text{If a, b, c, d,... is a geometric sequence, then}\ (b)/(a)=(c)/(b)=(d)/(c)\\\\Sequence\ 1:-10,\ 20,\ -40,\ 80,\ ...\\\\20-(-10)=20+10=30\\-40-20=-60\\not\ arithmetic\\\\(20)/(-10)=-2\\(-40)/(20)=-2\\(80)/(-40)=-2\\It's\ a\ geometric\ sequence\\\\Sequence\ 2:15,\ -5,\ -25,\ -45,\ ...\\\\-5-15=-20\\-25-(-5)=-25+5=-20\\-45-(-25)=-45+25=-20\\It's\ an\ arithmetic\ sequence}`

`(-5)/(15)=-(1)/(3)\\(-25)/(-5)=5\\not\ geometric\\\\\\Answer:\ \boxed{A.\text{Sequence 2 is arithmetic and Sequence 1 is geometric}}`