dari suatu barisan geometri diketahui suku ke-5 adalah 25 dan suku ke 7 adalah 625. suku ke-30 barisan tersebut adalah

[tex] \frac{u7}{u5} = \frac{625}{25} \\ \frac{a {r }^{6} }{a {r}^{4} } = 25 \\ {r }^{2} = 25 \\ r = \sqrt{25} \\ r = 5[/tex]


[tex]u5 = 25 \\ a {r}^{4} = 25 \\ a {(5)}^{4} = 25 \\ a = \frac{ {5}^{2} }{ {5}^{4} } = \frac{1}{ {5}^{2} } = \frac{1}{25} [/tex]


[tex]u30 = a {r}^{29} \\ = \frac{1}{25} \times {5}^{29} \\ = \frac{ {5}^{29} }{ {5}^{2} } = {5}^{29 - 2} = {5}^{27} \\[/tex]

U5 = ar^4
25 = ar^4

U7 = ar^6
625 = ar^6

ar^6/ar^4 = 625/25
r^2 = 25
r = V25
r = 5

ar^4 = 25
a(5^4) = 25
625a = 25
a = 25/625
a = 1/25

U30 = ar^29
U30 = 1/25 (5^29)
U30 = 5^(-2) (5^29)
U30 = 5^27