Question

Find the next two terms of each geometric sequence (show work)

1. -15, -30, -6, __, __

2. 90, 30, 10, __, __

3. 1/4, 3/8, 9/16, __, __

Answer 1

`\huge\boxed{1.\ -120,\ -240}\\\boxed{2.\ (10)/(3),\ (10)/(9)}\\\boxed{3.\ (27)/(32),\ (81)/(64)}`

Explanation:

`\text{if}\\a_1,\ a_2,\ a_3,\ ...\text{is a geometric sequence}\\\text{then}\\\\(a_2)/(a_1)=(a_3)/(a_2)=(a_4)/(a_3)=...=(a_n)/(a_(n-1))=const.=r\\\\a_n=a_(n-1)r`

`1.\\-15,\ -30,\ -6\\\\(-30)/(-15)=-2;\ (-6)/(-30)=(1)/(5)`

it,s not a geometric sequence...

I think it should be:

`-15,\ -30,\ -60,\ ...\\\\(-30)/(-15)=2;\ (-60)/(-30)=2\\\\next\\\\-60\cdot2=-120\\-120\cdot2=-240`

`2.\\90,\ 30,\ 10,\ ...\\\\(30)/(90)=(1)/(3);\ (10)/(30)=(1)/(3)\\\\next\\\\10\cdot(1)/(3)=(10)/(3)\\\\(10)/(3)\cdot(1)/(3)=(10)/(9)`

`3.\\(1)/(4),\ (3)/(8),\ (9)/(16),\ ...\\\\((3)/(8))/((1)/(4))=(3)/(8)\cdot(4)/(1)=(3)/(2);\ ((9)/(16))/((3)/(8))=(9)/(16)\cdot(8)/(3)=(3)/(2)\\\\next\\\\(9)/(16)\cdot(3)/(2)=(27)/(32)\\\\(27)/(32)\cdot(3)/(2)=(81)/(64)`