SOLUTION: what is the 8th term in the sequence -1/2, -1, -2, -4,...

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Question 1183906: what is the 8th term in the sequence -1/2, -1, -2, -4,...
Answer by MathLover1(20850) About Me  (Show Source):
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sequence -1%2F2, -1, -2, -4,...
The ratio between the consecutive terms is
r=-1%2F%28-1%2F2%29=2
r=-2%2F-1=2
=>this sequence is geometric, the ratio between the consecutive terms is constant
nth term:
a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29 ....where n=1,2,3,....
a%5B1%5D=-1%2F2
r=2
a%5Bn%5D=-%281%2F2%29%2A2%5E%28n+-1%29+
check given terms
a%5B1%5D=-%281%2F2%29%2A2%5E%281+-1%29+
a%5B1%5D=-%281%2F2%29%2A2%5E0+
a%5B1%5D=-%281%2F2%29%2A1+
a%5B1%5D=-%281%2F2%29+->true
a%5B2%5D=-%281%2F2%29%2A2%5E%282+-1%29+
a%5B2%5D=-%281%2F2%29%2A2%5E1+
a%5B2%5D=-%281%2F2%29%2A2+
a%5B2%5D=-1->true
a%5B3%5D=-%281%2F2%29%2A2%5E%283+-1%29+
a%5B3%5D=-%281%2F2%29%2A2%5E2+
a%5B3%5D=-%281%2F2%29%2A4+
a%5B3%5D=-2->true
then, the 8th term in the sequence will be
a%5B8%5D=-%281%2F2%29%2A2%5E%288+-1%29+
a%5B8%5D=-%281%2F2%29%2A2%5E7+
a%5B8%5D=-%281%2F2%29%2A128+
a%5B8%5D=-64