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

×
256

×
256

✓
512

×
512
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
256
256
512
512
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^2124x512=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