Question

Which sequence are geometric? Check all that apply

Answer 1

10, 7.5, 5.625, 4.21875, ...

160, 40, 10, 2.5, ...

20, 70, 245, 857.5, ...

5, 5.5, 6.05, 6.655, ...

Explanation:

`\text{If}\ a,\ b,\ c,\ d,\ e,\ ...\ \text{is a geometric sequence, then}\ (b)/(a)=(c)/(b)=(d)/(c)=(e)/(d)=....\\\\\#1\\\\(7.5)/(10)=0.75\\(5.625)/(7.5)=0.75\\(4.21875)/(5.625)=0.75\\\boxed{YES}\\================================\\`

`\#2\\\\(40)/(160)=(1)/(4)\\(10)/(40)=(1)/(4)\\(2.5)/(10)=(1)/(4)\\\boxed{YES}\\================================\\`

`\#3\\\\(70)/(20)=3.5\\(245)/(70)=3.5\\(857.5)/(245)=3.5\\\boxed{YES}\\================================\\`

`\#4\\\\(16.5)/(13)=(165)/(130)=(33)/(26)\\(20)/(16.5)=(200)/(165)=(40)/(33)\\eq(33)/(26)\\\boxed{NO}\\================================\\`

`\#5\\\\(5.5)/(5)=1.1\\(6.05)/(5.5)=1.1\\(6.655)/(6.05)=1.1\\\boxed{YES}\\================================\\`

`\#6\\\\(17.1)/(16)=1.06875\\(18.2)/(17.1)=1.0643274..\\eq1.06875\\\boxed{NO}`