设{a}是公差为正整数的等差数列,若a1+a2+a3=15,a1a2a3=80,求a11+a12+a13

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设{a}是公差为正整数的等差数列,若a1+a2+a3=15,a1*a2*a3=80,求a11+a12+a13

a1+a3=2a2
=>3a2=15
=>a2=5
a+d=5①
a1*a2*a3=80
a1^2*a2(1+2d)=80
=>a1^2*(1+2d)=16②
联立①②
解得,a1=2,a3=8 d=3
a11+a12+a13
=3a12
=3(a1+11d)
=3*(2+33)
=105

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