Question

Which sequence are geometric? Check all that apply

Answer 1

Answer:

10, 7.5, 5.625, 4.21875, ...

160, 40, 10, 2.5, ...

20, 70, 245, 857.5, ...

5, 5.5, 6.05, 6.655, ...

Step-by-step explanation:

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

$\#2\\\\\dfrac{40}{160}=\dfrac{1}{4}\\\dfrac{10}{40}=\dfrac{1}{4}\\\dfrac{2.5}{10}=\dfrac{1}{4}\\\boxed{YES}\\================================$

$\#3\\\\\dfrac{70}{20}=3.5\\\dfrac{245}{70}=3.5\\\dfrac{857.5}{245}=3.5\\\boxed{YES}\\================================$

$\#4\\\\\dfrac{16.5}{13}=\dfrac{165}{130}=\dfrac{33}{26}\\\dfrac{20}{16.5}=\dfrac{200}{165}=\dfrac{40}{33}\neq\dfrac{33}{26}\\\boxed{NO}\\================================$

$\#5\\\\\dfrac{5.5}{5}=1.1\\\dfrac{6.05}{5.5}=1.1\\\dfrac{6.655}{6.05}=1.1\\\boxed{YES}\\================================$

$\#6\\\\\dfrac{17.1}{16}=1.06875\\\dfrac{18.2}{17.1}=1.0643274..\neq1.06875\\\boxed{NO}$