Penjelasan dengan langkah-langkah:
Diketahui U₆ = 24 dan U₉ = 8.
Masukkan kedalam rumus,
=> U₆ = ar⁵
=> 24 = ar⁵
=> U₉ = ar⁸
=> 8 = ar⁸
Sekarang, bagilah U₉ dengan U₆, maka:
=> \frac{8}{24}=\frac{ar^{8}}{ar^{5}}
24
8
=
ar
5
ar
8
=> \frac{1}{3}=r^{3},r=\sqrt[3]{\frac{1}{3}}
3
1
=r
3
,r=
3
3
1
Jika rasio didapatkan, substitusi kedalam U₆ untuk mendapatkan nilai a, maka:
=> 24=ar^{5}24=ar
5
=> 24=a(\sqrt[3]{\frac{1}{3}})^{5}24=a(
3
3
1
)
5
=> 24=\frac{1}{3}a(\sqrt[3]{(\frac{1}{3})^{2}})24=
3
1
a(
3
(
3
1
)
2
)
=> 72=\sqrt[3]{(\frac{1}{3})^{2}}a72=
3
(
3
1
)
2
a
Pangkatkan tiga,
=> 72^{3}=(\frac{1}{9})a^{3}72
3
=(
9
1
)a
3
=> (72^{3})(3^{2})=a^{3}(72
3
)(3
2
)=a
3
=> a=72\sqrt[3]{9}a=72
3
9
Sekarang, tentukan suku ketiga,
=> U₃ = ar²
=> U₃ = (72\sqrt[3]{9})(\sqrt[3]{(\frac{1}{3})^{2}})(72
3
9
)(
3
(
3
1
)
2
)
=> U₃ = (72\sqrt[3]{9})(\sqrt[3]{(\frac{1}{9})})(72
3
9
)(
3
(
9
1
)
)
=> U₃ = 72\sqrt[3]{9(\frac{1}{9})}72
3
9(
9
1
)
=> U₃ = 72\sqrt[3]{1}72
3
1
=> U₃ = 72