an is a proportional series, a5 2S4 3 a6 2S5 3, find the common ratio q?

a5=2s45+3, s4=(a5-3) 2a6=2s5+3=2(s4+a5)+3=2s4+2a5+3 Substituting the above equation is obtained.

2*(a5-3)/2+2a5+3

a5-3+2a5+3=3a5

a6=q*a5=3a5, and q=3

is a proportional series.

a5=a1q^4 ， a6=a1q^5

a1q 4 = 2[a1(1-q 4) (1-q)] 3a1q 5 = 2[a1(1-q 5) (1-q)] 3 subtract the two formulas: a1q 4 - a1q 5 = [2a1(1-q 4) -2a1(1-q 5)] (1-q).

a1q^4(1-q) = (-2a1q^4 + 2a1q^5) / (1-q)

a1q^4(1-q) = [-2a1q^4(1-q)] / (1-q)

a1q^4(1-q) = -2a1q^4

1-q=-2q=3

a5=2s4+3 a.

a6=2s5+3 a5q=2s4+3 +2a5 two.

Simultaneous solution of equations.

Two - One a5q-a5=2a5 q=3

According to the proposition, an equation is established: 2aq3=aq5+aq4 (let a be the proportional series of annihilation.)

The first term, the common ratio is q).

Simplification obtains: the sail group q2 +q=2 (a, q are not zero) to solve this equation to obtain the state disadvantages: q=1 or -2

In the proportional sequence an, a4 = a 2, q = 2, then a6 =

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Because the ratio of the first male is q = -1 3

a1 + a3 + a5 + a7 is the first term of a1, the common ratio is 1 9 of the proportional number series of auspicious numbers a2 + a4 + a6 + a8 is the first term of a1q, the common ratio is 1 foot Shen 9 of the proportional series, so (a1 + a3 + a5 + a7) (a2 + a4 + a6 + a8) [a1 (1-1 9 4) (1-1 9)] a1 3) * (1-1 9 4) (1-1 9)].

Two minus one.

a1*q^4(q-1)=2a1*q^3

q(q-1)=2

q = - 1/2

Or 5/2 you can verify it.

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a5=2s4+3，a6=2s5+3

Subtract the two rulers to get the following

a6-a5=2(s5-s4)=2a5

Therefore a6=3a5

i.e. a6 a5=3

De: Lingzheng's husband has a clear material ratio of q=3

Obviously a5 = a4*q, a6 = a4*q

Then 2a4=a4*q -a4*q

For proportional series a4≠0

Then 2=q -q

The solution yields q=2 or q=-1

Replace a5 and a6 with keys to a4 to indicate sleepiness, about a4, and solve the ruler out q, that is, a6 = q 2 * a4 a5 = q * a4

The equation is converted to 2=q+q2

q=1 or q=-2

Correct answer: 2a4=a4*q +a4q

2=q+q^2

q=1 or q=-2