已知一個等比數列的第k項和公比分別是96和2。若首k項之和是189，k的值?(步驟)?

an=ar^(n-1)
==> ak=a*2^(k-1)=96=3*2^5
==>a=3 ,k=6

Sn=a(r^n -1)/(r-1)
==>Sk=3*(2^k-1)/(2-1)=189
==>k=6

r=2
T(k)=96
96=a(2)^(k-1) i
s=a(r^n -1)/(r-1)
189=a(2^k -1)/(2-1)
189=a(2^k -1) ii
i/ii
96/189=2^(k-1) / 2^(k) -1
32(2^k)-32=63[2^(k-1)]
64(2^k)-64=63(2^k)
2^k=64
k=6