Tentukan rasio dan suku keempat suatu barisan geometri jika diketahui
a. a = 2 dan U5 = 162
b. a = 4 dan U3 = 64
c. a = 7/2 dan U7 = 224
d. a = 1/15 dan U6 = 81/15
e. a = 90 dan U5 =10/9
tentukan suku yang diminta dari barisan geometri berikut ini.
a. 2, 10, 50, 250, ..., U7
b. 16, 8, 4, 2, ..., U8
a. a = 2 dan U5 = 162
b. a = 4 dan U3 = 64
c. a = 7/2 dan U7 = 224
d. a = 1/15 dan U6 = 81/15
e. a = 90 dan U5 =10/9
tentukan suku yang diminta dari barisan geometri berikut ini.
a. 2, 10, 50, 250, ..., U7
b. 16, 8, 4, 2, ..., U8
Kayzhen
![\bf \underline {Nomor\:1}\\\bf a). \:a = 2\:\:dan\:\:u5 = 162\\\\Maka:\\u5=a.r^4\\\\162=2.r^4\\\\ \frac{162}{2}=r^4\\\\81=r^4\\\\r= \sqrt[4]{81} \\\\r=3\\\\Sehingga:\\u4=a.r^3\\\\u4=2.3^3\\\\u4=2.27\\\\u4=54](https://tex.z-dn.net/?f=%5Cbf+%5Cunderline+%7BNomor%5C%3A1%7D%5C%5C%5Cbf+a%29.+%5C%3Aa+%3D+2%5C%3A%5C%3Adan%5C%3A%5C%3Au5+%3D+162%5C%5C%5C%5CMaka%3A%5C%5Cu5%3Da.r%5E4%5C%5C%5C%5C162%3D2.r%5E4%5C%5C%5C%5C+%5Cfrac%7B162%7D%7B2%7D%3Dr%5E4%5C%5C%5C%5C81%3Dr%5E4%5C%5C%5C%5Cr%3D+%5Csqrt%5B4%5D%7B81%7D+%5C%5C%5C%5Cr%3D3%5C%5C%5C%5CSehingga%3A%5C%5Cu4%3Da.r%5E3%5C%5C%5C%5Cu4%3D2.3%5E3%5C%5C%5C%5Cu4%3D2.27%5C%5C%5C%5Cu4%3D54 "\bf \underline {Nomor\:1}\\\bf a). \:a = 2\:\:dan\:\:u5 = 162\\\\Maka:\\u5=a.r^4\\\\162=2.r^4\\\\ \frac{162}{2}=r^4\\\\81=r^4\\\\r= \sqrt[4]{81} \\\\r=3\\\\Sehingga:\\u4=a.r^3\\\\u4=2.3^3\\\\u4=2.27\\\\u4=54")
![\bf c). \:a = \frac{7}{2}\:\:dan\:\:u7 = 224\\\\Maka:\\u7=a.r^6\\\\224= \frac{7}{2} .r^6\\\\ 224\times \frac{2}{7} =r^6\\\\64=r^6\\\\r= \sqrt[6]{64} \\\\r=2\\\\Sehingga:\\u4=a.r^3\\\\u4= \frac{7}{2} .2^3\\\\u4= \frac{7}{2} .8\\\\u4=28](https://tex.z-dn.net/?f=%5Cbf+c%29.+%5C%3Aa+%3D+%5Cfrac%7B7%7D%7B2%7D%5C%3A%5C%3Adan%5C%3A%5C%3Au7+%3D+224%5C%5C%5C%5CMaka%3A%5C%5Cu7%3Da.r%5E6%5C%5C%5C%5C224%3D+%5Cfrac%7B7%7D%7B2%7D+.r%5E6%5C%5C%5C%5C+224%5Ctimes+%5Cfrac%7B2%7D%7B7%7D+%3Dr%5E6%5C%5C%5C%5C64%3Dr%5E6%5C%5C%5C%5Cr%3D+%5Csqrt%5B6%5D%7B64%7D+%5C%5C%5C%5Cr%3D2%5C%5C%5C%5CSehingga%3A%5C%5Cu4%3Da.r%5E3%5C%5C%5C%5Cu4%3D+%5Cfrac%7B7%7D%7B2%7D+.2%5E3%5C%5C%5C%5Cu4%3D+%5Cfrac%7B7%7D%7B2%7D+.8%5C%5C%5C%5Cu4%3D28 "\bf c). \:a = \frac{7}{2}\:\:dan\:\:u7 = 224\\\\Maka:\\u7=a.r^6\\\\224= \frac{7}{2} .r^6\\\\ 224\times \frac{2}{7} =r^6\\\\64=r^6\\\\r= \sqrt[6]{64} \\\\r=2\\\\Sehingga:\\u4=a.r^3\\\\u4= \frac{7}{2} .2^3\\\\u4= \frac{7}{2} .8\\\\u4=28")
![\bf d). \:a = \frac{1}{15}\:\:dan\:\:u6 = \frac{81}{15}\\\\Maka:\\u6=a.r^5\\\\ \frac{81}{15} = \frac{1}{15} .r^5\\\\ \frac{81}{15}\times \frac{15}{1} =r^5\\\\81=r^5\\\\r= \sqrt[5]{81}\\\\Sehingga:\\u4=a.r^3\\\\u4= \frac{1}{15} .(\sqrt[5]{81})^3 \\\\u4= \frac{1}{15} .81^{ \frac{3}{5} }](https://tex.z-dn.net/?f=%5Cbf+d%29.+%5C%3Aa+%3D+%5Cfrac%7B1%7D%7B15%7D%5C%3A%5C%3Adan%5C%3A%5C%3Au6+%3D+%5Cfrac%7B81%7D%7B15%7D%5C%5C%5C%5CMaka%3A%5C%5Cu6%3Da.r%5E5%5C%5C%5C%5C+%5Cfrac%7B81%7D%7B15%7D+%3D+%5Cfrac%7B1%7D%7B15%7D+.r%5E5%5C%5C%5C%5C+%5Cfrac%7B81%7D%7B15%7D%5Ctimes+%5Cfrac%7B15%7D%7B1%7D+%3Dr%5E5%5C%5C%5C%5C81%3Dr%5E5%5C%5C%5C%5Cr%3D+%5Csqrt%5B5%5D%7B81%7D%5C%5C%5C%5CSehingga%3A%5C%5Cu4%3Da.r%5E3%5C%5C%5C%5Cu4%3D+%5Cfrac%7B1%7D%7B15%7D+.%28%5Csqrt%5B5%5D%7B81%7D%29%5E3+%5C%5C%5C%5Cu4%3D+%5Cfrac%7B1%7D%7B15%7D+.81%5E%7B+%5Cfrac%7B3%7D%7B5%7D+%7D "\bf d). \:a = \frac{1}{15}\:\:dan\:\:u6 = \frac{81}{15}\\\\Maka:\\u6=a.r^5\\\\ \frac{81}{15} = \frac{1}{15} .r^5\\\\ \frac{81}{15}\times \frac{15}{1} =r^5\\\\81=r^5\\\\r= \sqrt[5]{81}\\\\Sehingga:\\u4=a.r^3\\\\u4= \frac{1}{15} .(\sqrt[5]{81})^3 \\\\u4= \frac{1}{15} .81^{ \frac{3}{5} }")
![\bf e). \:a = 90\:\:dan\:\:u5 = \frac{10}{9}\\\\Maka:\\u5=a.r^4\\\\\frac{10}{9}=90.r^4\\\\ \frac{10}{9}\times \frac{1}{90}=r^4\\\\\frac{1}{81}=r^4\\\\r= \sqrt[4]{\frac{1}{81}} \\\\r=\frac{1}{3}\\\\Sehingga:\\u4=a.r^3\\\\u4=90.(\frac{1}{3})^3\\\\u4=90.\frac{1}{27}\\\\u4=\frac{10}{3}](https://tex.z-dn.net/?f=%5Cbf+e%29.+%5C%3Aa+%3D+90%5C%3A%5C%3Adan%5C%3A%5C%3Au5+%3D+%5Cfrac%7B10%7D%7B9%7D%5C%5C%5C%5CMaka%3A%5C%5Cu5%3Da.r%5E4%5C%5C%5C%5C%5Cfrac%7B10%7D%7B9%7D%3D90.r%5E4%5C%5C%5C%5C+%5Cfrac%7B10%7D%7B9%7D%5Ctimes+%5Cfrac%7B1%7D%7B90%7D%3Dr%5E4%5C%5C%5C%5C%5Cfrac%7B1%7D%7B81%7D%3Dr%5E4%5C%5C%5C%5Cr%3D+%5Csqrt%5B4%5D%7B%5Cfrac%7B1%7D%7B81%7D%7D+%5C%5C%5C%5Cr%3D%5Cfrac%7B1%7D%7B3%7D%5C%5C%5C%5CSehingga%3A%5C%5Cu4%3Da.r%5E3%5C%5C%5C%5Cu4%3D90.%28%5Cfrac%7B1%7D%7B3%7D%29%5E3%5C%5C%5C%5Cu4%3D90.%5Cfrac%7B1%7D%7B27%7D%5C%5C%5C%5Cu4%3D%5Cfrac%7B10%7D%7B3%7D "\bf e). \:a = 90\:\:dan\:\:u5 = \frac{10}{9}\\\\Maka:\\u5=a.r^4\\\\\frac{10}{9}=90.r^4\\\\ \frac{10}{9}\times \frac{1}{90}=r^4\\\\\frac{1}{81}=r^4\\\\r= \sqrt[4]{\frac{1}{81}} \\\\r=\frac{1}{3}\\\\Sehingga:\\u4=a.r^3\\\\u4=90.(\frac{1}{3})^3\\\\u4=90.\frac{1}{27}\\\\u4=\frac{10}{3}")
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Thanks 94
ikhwanafina
ka yg d nomor 1 kata guruku U6 nya diganti U5
Kayzhen
ia dek.. yg no. 1 bagian d mank agak aneh. . .
ini jawabannya klo u nya diganti u5 ..
Kayzhen
u5 = a x r^4
81/15 = 1/15 x r^4
81/15 x 15/1 = r^4
81 = r^4
r = akar pangkat 4 dari 81
r = 3
.
Sehingga:
u4 = a x r^3
u4 = 1/15 x 3^3
u4 = 27/15 <--- jawabannya
ariftampan
itu u4 dari mana itu?
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