seutas tali di potong menjadi 6 bagian dan panjang potongan tali membentuk barisan geometri . jikaa panjang potongan tali kedua dan kelima berturut turut 10 cm

Barisan geometri
[tex] U_{2} [/tex] = 10 cm
[tex] U_{5} [/tex] = 80 cm
[tex] S_{6} [/tex] = ?

[tex] U_{n} [/tex] = a.[tex] r^{n-1} [/tex]
[tex] U_{2} [/tex] = a.[tex] r^{1} [/tex]
[tex] U_{5} [/tex] = a.[tex] r^{4} [/tex]

[tex] \frac{a.r}{a. r^{4}} [/tex] = [tex] \frac{10}{80} [/tex]
8.a.r = a.[tex] r^{4} [/tex]
8 = [tex] \frac{a. r^{4} }{a.r} [/tex]
8 = [tex] r^{3} [/tex]
[tex] \sqrt[3]{8} [/tex] = r
2 = r

[tex] U_{2} [/tex] = a.r
10 = a.2
[tex] \frac{10}{2} [/tex] = a
5 = a

[tex] U_{1} [/tex] = a
[tex] U_{1} [/tex] = 5

[tex] S_{n} [/tex] = a.[tex] \frac{ r^{n}-1 }{r-1} [/tex]
[tex] S_{6} [/tex] = 5.[tex] \frac{ 2^{6}-1 }{2-1} [/tex]
[tex] S_{6} [/tex] = 5.[tex] \frac{64-1}{1} [/tex]
[tex] S_{6} [/tex] = 5.63
[tex] S_{6} [/tex] = 315

U2 = 10
ar = 10

U5 = 80
ar⁴ = 80

U5:U2 = 80:10
(ar⁴):(ar) = 8
r³ = 8
r = 2


U2 = 10
ar = 10
a(2) = 10
a = 5


S6 = [a(rⁿ - 1)]/(r - 1)
S6 = [5(2^6 - 1)]/(2 - 1)
S6 = [5(64 - 1)]/1
S6 = 5(63)
S6 = 315 cm.