Question 1156701: Three consecutive terms of a geometric sequence are:
2a-2,2a+2,5a+1. Determine the value
of each of the terms. Use these term values to determine the equation(s) for the general term of
the sequence (tn). (think quadratic)
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! adjacent terms have the same ratio
so (2a+2)/(2a-2)=(5a+1)/(2a+2)
Therefore,
4a^2+8a+4=10a^2-8a-2
so 0=6a^2-16a-6
or 3a^2-8a-3=0
(3a+1)(a-3)=0
a=3, or -1/3
the terms are 4, 8, 16 with common ratio 2 or -8/3, 4/3, -2/3 with common ratio -1/2
a, ar, ar^2,...or
4*2^r for r>=0
(-1)^r*(8/3)*(1/2)^(r-1) for r=1, 2,3,...
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
In a geometric sequence, the ratio of consecutive terms is constant. So in this problem,
Cross multiply and solve the resulting quadratic equation.
You can finish from there.
(1) Finding the values of the terms....
There will be two solutions, resulting in two different sequences.
(2) Determining the equations for the general terms of the two sequences....
The three consecutive terms in each sequence will only tell us the common ratio between the terms. Without knowing WHICH terms of the sequence these terms are, we have no way of knowing the first term of the sequence; therefore we can't determine the formula for the sequence.
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