等差等比(1題)

(a)
R1,R2,R3 是等比數列, 即 R2/R1 = R3/R2 = r
可寫 Rn = R1*r^(n-1)

C1 = 2πR1
C2 = 2πR2 = 2πR1*r
C3 = 2πR3 = 2πR1*r²

Cn = 2πRn = 2πR1*r^(n-1)
C{n-1} = 2πR{n-1} = 2πR1*r^(n-2)

Cn/C{n-1} = 2πR1*r^(n-1) / [2πR1*r^(n-2)] = r

所以 C1, C2, C3 也是等比數列。
Cn = C1 * r^(n-1)


(b)
C3 = 4π = C1 * r^(2)
C6 = 0.0625π = C1 * r^(5)
C(k) = 64π

C6/C3 得出 0.015625 = r^3
r = 0.25

4π = C1 * 0.25²
C1 = 64π

C(k) = C1 * r^(k-1)
C(k) = 64π * r^(k-1) = 64π
r^(k-1) = 1
k-1 = 0
k = 1