Answer: ![\bold{(1)\ \dfrac{19,683}{64}\qquad (2)\ 16}](https://tex.z-dn.net/?f=%5Cbold%7B%281%29%5C%20%5Cdfrac%7B19%2C683%7D%7B64%7D%5Cqquad%20%282%29%5C%2016%7D)
<u>Step-by-step explanation:</u>
(1) (12, 18, 27, ...)
The common ratio is:
![r=\dfrac{a_{n+1}}{a_n}\quad r =\dfrac{18}{12}=\boxed{\dfrac{3}{2}}\quad \rightarrow \quad r=\dfrac{27}{18}=\boxed{\dfrac{3}{2}}](https://tex.z-dn.net/?f=r%3D%5Cdfrac%7Ba_%7Bn%2B1%7D%7D%7Ba_n%7D%5Cquad%20r%20%3D%5Cdfrac%7B18%7D%7B12%7D%3D%5Cboxed%7B%5Cdfrac%7B3%7D%7B2%7D%7D%5Cquad%20%5Crightarrow%20%5Cquad%20r%3D%5Cdfrac%7B27%7D%7B18%7D%3D%5Cboxed%7B%5Cdfrac%7B3%7D%7B2%7D%7D)
The equation is:
![a_n=a_o(r)^{n-1}\\\\Given:a_o=12,\ r=\dfrac{3}{2}\\\\\\Equation:\\a_n =12\bigg(\dfrac{3}{2}\bigg)^{n-1}\\\\\\\\9th\ term:\\a_9=12\bigg(\dfrac{3}{2}\bigg)^{9-1}\\\\\\a_9=12\bigg(\dfrac{3}{2}\bigg)^{8}\\\\\\.\quad =\large\boxed{\dfrac{19643}{64}}](https://tex.z-dn.net/?f=a_n%3Da_o%28r%29%5E%7Bn-1%7D%5C%5C%5C%5CGiven%3Aa_o%3D12%2C%5C%20%20r%3D%5Cdfrac%7B3%7D%7B2%7D%5C%5C%5C%5C%5C%5CEquation%3A%5C%5Ca_n%20%3D12%5Cbigg%28%5Cdfrac%7B3%7D%7B2%7D%5Cbigg%29%5E%7Bn-1%7D%5C%5C%5C%5C%5C%5C%5C%5C9th%5C%20term%3A%5C%5Ca_9%3D12%5Cbigg%28%5Cdfrac%7B3%7D%7B2%7D%5Cbigg%29%5E%7B9-1%7D%5C%5C%5C%5C%5C%5Ca_9%3D12%5Cbigg%28%5Cdfrac%7B3%7D%7B2%7D%5Cbigg%29%5E%7B8%7D%5C%5C%5C%5C%5C%5C.%5Cquad%20%3D%5Clarge%5Cboxed%7B%5Cdfrac%7B19643%7D%7B64%7D%7D)
![(2)\qquad \bigg(\dfrac{1}{16},\dfrac{1}{8},\dfrac{1}{4},\dfrac{1}{2}\bigg)\\\\\\\text{The common ratio is}:\\\\r=\dfrac{a_{n+1}}{a_n}\quad r=\dfrac{\frac{1}{8}}{\frac{1}{16}}=\boxed{2}\quad \rightarrow \quad r=\dfrac{\frac{1}{4}}{\frac{1}{8}}=\boxed{2}](https://tex.z-dn.net/?f=%282%29%5Cqquad%20%5Cbigg%28%5Cdfrac%7B1%7D%7B16%7D%2C%5Cdfrac%7B1%7D%7B8%7D%2C%5Cdfrac%7B1%7D%7B4%7D%2C%5Cdfrac%7B1%7D%7B2%7D%5Cbigg%29%5C%5C%5C%5C%5C%5C%5Ctext%7BThe%20common%20ratio%20is%7D%3A%5C%5C%5C%5Cr%3D%5Cdfrac%7Ba_%7Bn%2B1%7D%7D%7Ba_n%7D%5Cquad%20%20r%3D%5Cdfrac%7B%5Cfrac%7B1%7D%7B8%7D%7D%7B%5Cfrac%7B1%7D%7B16%7D%7D%3D%5Cboxed%7B2%7D%5Cquad%20%5Crightarrow%20%5Cquad%20r%3D%5Cdfrac%7B%5Cfrac%7B1%7D%7B4%7D%7D%7B%5Cfrac%7B1%7D%7B8%7D%7D%3D%5Cboxed%7B2%7D)
The equation is:
![a_n=a_o(r)^{n-1}\\\\Given:a_o=\dfrac{1}{16},\ r=2\\\\\\Equation:\\a_n =\dfrac{1}{16}(2)^{n-1}\\\\\\\\9th\ term:\\a_9=\dfrac{1}{16}(2)^{9-1}\\\\\\a_9=\dfrac{1}{16}(2)^{8}\\\\\\.\quad =\large\boxed{16}](https://tex.z-dn.net/?f=a_n%3Da_o%28r%29%5E%7Bn-1%7D%5C%5C%5C%5CGiven%3Aa_o%3D%5Cdfrac%7B1%7D%7B16%7D%2C%5C%20%20r%3D2%5C%5C%5C%5C%5C%5CEquation%3A%5C%5Ca_n%20%3D%5Cdfrac%7B1%7D%7B16%7D%282%29%5E%7Bn-1%7D%5C%5C%5C%5C%5C%5C%5C%5C9th%5C%20term%3A%5C%5Ca_9%3D%5Cdfrac%7B1%7D%7B16%7D%282%29%5E%7B9-1%7D%5C%5C%5C%5C%5C%5Ca_9%3D%5Cdfrac%7B1%7D%7B16%7D%282%29%5E%7B8%7D%5C%5C%5C%5C%5C%5C.%5Cquad%20%3D%5Clarge%5Cboxed%7B16%7D)
A(5) = 2 + 5^2 = 2 + 25 = 27
Step-by-step explanation:
This sequence is defined as a(n) = 2 + n^2.
Thus, a(1) = 2 + 1^2 = 2 + 1 = 3
Then a(5) = 2 + 5^2 = 2 + 25 = 27
Answer:
option D :
f(-8) = -2 ; f(4) = 3
Step-by-step explanation:
f(-8) = ³√-8 = -2
f(4) = 3 (the constant function)
Answer:
$2.60
Step-by-step explanation:
first you need to see how many time 2.90 goes into 20 it is 6, so then you multiply 2.90 times 6 and get 17.40. Lastly you subtract 17.40 from 20 to get 2.60
Hope this helps
Answer:
The LCM of 9, 12, and 24, is <em>72. </em>
Step-by-step explanation:
To find the answer you must figure out the factors of <em>each number</em>, and see which factor has the <em>same number.</em>
<u><em>Factors of 9: </em></u> <u><em>Factors of 12:</em></u><em> </em><u><em>Factors of 24: </em></u>
<em> 9 12 24</em>
<em> 18 24 48</em>
<em> 27 36 72</em>
<em> 36 48</em>
<em> 45 60</em>
<em> 54 72</em>
<em> 63</em>
<em> 72</em>
When we look at all these factors, none of them have the same number <em>except 72.</em> Since <em>all</em> of these factors have <em>72 in them</em>, this is the<em> </em>LCM of 9, 12, and 24.