Diketahui 3 suku deret geometri , jumlah suku sukunya adalah 21 dan hasil kali suku sukunya adlah 216 . nilai terbesar dari suku deret geometri tersebut adalah
izharulhaq78
![\displaystyle u_1u_2u_3=a\times ar\times ar^2\\216=a^3r^3\\216=(ar)^3\\\sqrt[3]{216}=ar\\6=ar\\\\a+ar+ar^2=21\\a+6+ar^2=15\\a+ar^2=15\\a(1+r^2)=15\\a=\frac{15}{1+r^2}\\\\ar=6\\\frac{15}{1+r^2}\times r=6\\15r=6(1+r^2)\\5r=2(1+r^2)\\5r=2+2r^2\\0=2r^2-5r+2\\0=2r^2-4r-r+2\\0=2r(r-2)-1(r-2)\\0=(2r-1)(r-2)\\r=2\text{ atau }r=\frac12\\\\\diamond r=2\\ar^2=ar\times r\\ar^2=6\times2\\\boxed{\boxed{ar^2=12}}\\\\\diamond r=\frac12\\ar=6\\a\times\frac12=6\\a=6\times2\\\boxed{\boxed{a=12}}](https://tex.z-dn.net/?f=%5Cdisplaystyle+u_1u_2u_3%3Da%5Ctimes+ar%5Ctimes+ar%5E2%5C%5C216%3Da%5E3r%5E3%5C%5C216%3D%28ar%29%5E3%5C%5C%5Csqrt%5B3%5D%7B216%7D%3Dar%5C%5C6%3Dar%5C%5C%5C%5Ca%2Bar%2Bar%5E2%3D21%5C%5Ca%2B6%2Bar%5E2%3D15%5C%5Ca%2Bar%5E2%3D15%5C%5Ca%281%2Br%5E2%29%3D15%5C%5Ca%3D%5Cfrac%7B15%7D%7B1%2Br%5E2%7D%5C%5C%5C%5Car%3D6%5C%5C%5Cfrac%7B15%7D%7B1%2Br%5E2%7D%5Ctimes+r%3D6%5C%5C15r%3D6%281%2Br%5E2%29%5C%5C5r%3D2%281%2Br%5E2%29%5C%5C5r%3D2%2B2r%5E2%5C%5C0%3D2r%5E2-5r%2B2%5C%5C0%3D2r%5E2-4r-r%2B2%5C%5C0%3D2r%28r-2%29-1%28r-2%29%5C%5C0%3D%282r-1%29%28r-2%29%5C%5Cr%3D2%5Ctext%7B+atau+%7Dr%3D%5Cfrac12%5C%5C%5C%5C%5Cdiamond+r%3D2%5C%5Car%5E2%3Dar%5Ctimes+r%5C%5Car%5E2%3D6%5Ctimes2%5C%5C%5Cboxed%7B%5Cboxed%7Bar%5E2%3D12%7D%7D%5C%5C%5C%5C%5Cdiamond+r%3D%5Cfrac12%5C%5Car%3D6%5C%5Ca%5Ctimes%5Cfrac12%3D6%5C%5Ca%3D6%5Ctimes2%5C%5C%5Cboxed%7B%5Cboxed%7Ba%3D12%7D%7D "\displaystyle u_1u_2u_3=a\times ar\times ar^2\\216=a^3r^3\\216=(ar)^3\\\sqrt[3]{216}=ar\\6=ar\\\\a+ar+ar^2=21\\a+6+ar^2=15\\a+ar^2=15\\a(1+r^2)=15\\a=\frac{15}{1+r^2}\\\\ar=6\\\frac{15}{1+r^2}\times r=6\\15r=6(1+r^2)\\5r=2(1+r^2)\\5r=2+2r^2\\0=2r^2-5r+2\\0=2r^2-4r-r+2\\0=2r(r-2)-1(r-2)\\0=(2r-1)(r-2)\\r=2\text{ atau }r=\frac12\\\\\diamond r=2\\ar^2=ar\times r\\ar^2=6\times2\\\boxed{\boxed{ar^2=12}}\\\\\diamond r=\frac12\\ar=6\\a\times\frac12=6\\a=6\times2\\\boxed{\boxed{a=12}}")
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miftakhairat
trima kasih yahh
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