now, let's recall that a geometric sequence is one that uses some "r" common ratio to get the next term, by simply multiplying the current term by it.
![\bf \begin{array}{|cl|ll} \cline{1-2} term&value\\ \cline{1-2} a_1&\underline{\qquad }\\&\\ a_2&6\\&\\ a_3&\underline{6(r)}\\&\\ a_4&6(r)(r)\\&\\ &54\\ \cline{1-2} \end{array}\qquad \implies \begin{array}{llll} 54=6r^2\implies \cfrac{54}{6}=r^2\implies 9=r^2\\\\ \sqrt{9}=r\implies 3=r \end{array} \\\\[-0.35em] ~\dotfill\\\\ a_1=6\div 3\implies a_1=2~\hfill a_3=6(3)\implies a_3=18](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7B%7Ccl%7Cll%7D%20%5Ccline%7B1-2%7D%20term%26value%5C%5C%20%5Ccline%7B1-2%7D%20a_1%26%5Cunderline%7B%5Cqquad%20%7D%5C%5C%26%5C%5C%20a_2%266%5C%5C%26%5C%5C%20a_3%26%5Cunderline%7B6%28r%29%7D%5C%5C%26%5C%5C%20a_4%266%28r%29%28r%29%5C%5C%26%5C%5C%20%2654%5C%5C%20%5Ccline%7B1-2%7D%20%5Cend%7Barray%7D%5Cqquad%20%5Cimplies%20%5Cbegin%7Barray%7D%7Bllll%7D%2054%3D6r%5E2%5Cimplies%20%5Ccfrac%7B54%7D%7B6%7D%3Dr%5E2%5Cimplies%209%3Dr%5E2%5C%5C%5C%5C%20%5Csqrt%7B9%7D%3Dr%5Cimplies%203%3Dr%20%5Cend%7Barray%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20a_1%3D6%5Cdiv%203%5Cimplies%20a_1%3D2~%5Chfill%20a_3%3D6%283%29%5Cimplies%20a_3%3D18)
and of course, the next term or a₅ = 54(3) --> a₅ = 162.
Answer:
B: 6 units
Step-by-step explanation:
just took the test
Answer: $135
Step-by-step explanation: 48% of $355 would be 170 so therefore the $135 would be the cheaper penalty
Answer:
D) 3 1/8, 8 1/5, 8 1/3
Step-by-step explanation:
The order of the puppies' weights from least to greatest is the following:
![3\frac{1}{8} , 8\frac{1}{5}, 8\frac{1}{3}](https://tex.z-dn.net/?f=3%5Cfrac%7B1%7D%7B8%7D%20%2C%208%5Cfrac%7B1%7D%7B5%7D%2C%208%5Cfrac%7B1%7D%7B3%7D)
Three wholes are less than eight wholes, which means that the puppy named Kenadi weighs the least.
Scout and Major weigh a bit more than eight pounds. However, Major weighs less than Scout because one fifth is less than one third.
![8\frac{1}{5} < 8\frac{1}{3}](https://tex.z-dn.net/?f=8%5Cfrac%7B1%7D%7B5%7D%20%3C%208%5Cfrac%7B1%7D%7B3%7D)
This is why the correct option is D.