SOLUTION: in a geometric sequence the fourth term is 8 and the tenth term is 512. if common ratio is negative, find the first three terms.

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Question 378767: in a geometric sequence the fourth term is 8 and the tenth term is 512. if common ratio is negative, find the first three terms.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,

For a Geometric Sequence with common ratio= r a%5Bn%5D+=+a%5B1%5D%2Ar%5E%28n-1%29 Question States

a%5B4%5D+=+a%5B1%5D%2Ar%5E%284-1%29=8

r%5E3+=+8%2Fa%5B1%5D

a%5B10%5D+=+a%5B1%5D%2Ar%5E%2810-1%29=+a%5B1%5D%2Ar%5E%289%29=++512 

%28a%5B1%5D%2Fa%5B1%5D%5E3%29%2A8%5E3=+512

+a%5B1%5D%5E2=+1+

a%5B1%5D+=+-1 as the and common ratio is given as negative r%5E3+=+8 r= -2



CHECKING our answer by reviewing the first 10 terms of this sequence:

 -1, 2, -4, 8, -16, 32, -64, 128, -256, 512