已知数列(an)为等比数列,sn是它的前n项和,若a2*a3=2a1且a4与2a7的等差中项为5/4,则s5=?
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已知数列(an)为等比数列,sn是它的前n项和,若a2*a3=2a1且a4与2a7的等差中项为5/4,则s5=?
an= a1q^(n-1)
Sn = a1(q^n-1)/(q-1)
a2.a3 = 2a1
(a1^2) q^3 = 2a1
a1q^3 = 2 (1)
(a4+2a7)/2 = 5/4
a1q^3(1-2q^3) = 10/4
2(1-2q^3) = 10/4
4-8q^3=5
q^3 = -1/8
q = -1/2
a1= -16
S5 = a1(1-q^5)/(1-q)
= -16( 1- (-1/2)^5 ) / (3/2)
= (-32/3)( 33/32)
= -11
Sn = a1(q^n-1)/(q-1)
a2.a3 = 2a1
(a1^2) q^3 = 2a1
a1q^3 = 2 (1)
(a4+2a7)/2 = 5/4
a1q^3(1-2q^3) = 10/4
2(1-2q^3) = 10/4
4-8q^3=5
q^3 = -1/8
q = -1/2
a1= -16
S5 = a1(1-q^5)/(1-q)
= -16( 1- (-1/2)^5 ) / (3/2)
= (-32/3)( 33/32)
= -11
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