If $$\{a_n\}$$ is a geometric sequence in which $$a_4\cdotp a_7=-512 $$, $$a_3+a_8=124$$, and its common ratio $$q\in Z$$, then $$a_{10}=$$ is

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Uniteasy Admin · Accepted Answer

Since  $$\{a_n\}$$ is a geometric sequence
$$a_4\cdotp a_7=a_3\cdotp a_8=-512$$
and
$$a_3+a_8=124$$
Therefore,$$ a_3, a_8$$ are two real roots of the quadratic equation
$$ x^2-124x-512=0$$
Solve the function
$$ a_3= -4,a_8=128$$ or $$a_3=128, a_8= -4 $$
$$q^5=a_8/a_3= -32$$ or $$-1/32$$
$$q = -2$$ or $$q = -1/2$$ (cancel as $$q \in Z$$) 
$$a_{10}=a_3\cdotp q^7=(-4)\cdotp  (-2)^7=512 $$
C is the choice

Multiple Choice Question (MCQ)

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