4. Lima bilangan membentuk barisan geometri dengan Ut = 8 dan U5 = 162, tentukan U4

4. Lima bilangan membentuk barisan geometri dengan Ut = 8 dan U5 = 162, tentukan U4

Jawab:

Penjelasan dengan langkah-langkah:

$U_{t} =sqrt{U_{1}.U_{n} }$

$U_{t} =sqrt{U_{1}.U_{5} }$

$8 =sqrt{U_{1}.162 }$

$8^{2} ={U_{1}.162 }$

$64 ={U_{1}.162 }$

$U_{1} =frac{64}{162}$

$U_{1} =a=frac{32}{81}$

$U_{5} =a.r^{4}$

$162 =frac{32}{81} .r^{4}$

$r^{4} =frac{81}{32} .162$

$r^{4} =frac{81}{32} .2.81$

$r^{4} =frac{81.81}{16}$

$r^{4} =frac{3^{4} .3^{4} }{2^{4} }$

$r^{4} =frac{3^{8} }{2^{4} }$

$r =frac{9} {2 }$

$U_{4} =a.r^{3}$

$U_{4} =frac{32}{81} .(frac{9}{2}) ^{3}$

$U_{4} =frac{2^{5} }{9^{2} } .frac{9^{3} }{2^{3} }$

$U_{4} =4.9=36$