Arithmetic Geometric Sequence

2007-11-25 11:56 pm
1. The 3rd and 5th terms of a geometric sequence are 60 and 15 respectively . Find the sum to infinity of the geometric sequence if all the terms of the sequence are positive.
A.160
B. 240
C. 320
D. 480

2. If x^2 , -x^2 , -3x^3 , ... is a geometric sequence and x unequal 0 , find the value of x
A. 3
B. -3
C. - 1/3
D. 1/3

回答 (1)

2007-11-26 12:07 am
✔ 最佳答案
1.
the general term of Geometric Sequence = aRn-1
The 3rd and 5th terms of a geometric sequence are 60 and 15 respectively
aR2=60---------1
aR4=15---------2
1/2:
1/R2=4
R=1/2 or R=-1/2 (rejected) [all the terms are positive]
when R=1/2, a=240
the sum to infinity of the geometric sequence
=a/(1-R)
=240/(1-1/2)
=480
Answer : D
2.
x^2 , -x^2 , -3x^3 , ... is a geometric sequence
-x^2/x^2=-3x^3/-x^2
-1=3x
x=-1/3
Answer : C


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