geometric sequence

Itis given that 15 and -75 are the 5th term and the 6th term of a geometric
sequence respectively.
Find the 4th ,the 7th and the general term of thesequence.


Let a and r be the first term (T(1)) and the common ratio respectively.

T(5):
ar^4 = 15 ...... (1)

T(6):
ar^5 = -75 ...... (2)

(2)/(1):
r = -5

Put r = -5 into (1) :
a(-5)^4 = 15
625a = 15
a = 3/125

The 4th term, T(4)
= T(5)/r
= 15/(-5)
= -3

The 7th term, T(7)
= T(6) ´ r
= (-75) ´ (-5)
= 375

General term, T(n)
= (3/125) ´ (-5)^(n - 1)
= (-1)^(n - 1) ´ 3 ´ 5^(n - 4)

2011-10-25 00:58:53 補充：
^ 是次方的符號。
ar^4 = a 乘以 r 的 4 次方

ar^4=15
ar^5=-75
r = -5, a = 0.024
General term = 0.024 x (-5)^n-1
4th = -3, 7th = 375