An is an equal ratio sequence, A4, a7 = 2, a5a6 = - 8, find A1, a10

An is an equal ratio sequence, A4, a7 = 2, a5a6 = - 8, find A1, a10

From a5a6 = - 8 to a4a7 = - 8
∴a4a7=-8 ①
a4+a7=2 ②
We can get A4 = - 2a7 = 4q ^ 3 = - 2A1 = 1 by simultaneous methods
a1+a10=a1+a1q^9=a1+a1(q^3)^3=1+1x(-2)^3=-7
Four times the difference of a number minus five is exactly three times the number. The number is five
As above
Let this number be X
that
4(x-5)=3x
4x-20=3x
x=20
This number is 20
Let this number be X
4(x-5)=3x
x=20
(x-5)*4=3x
x=20
It is known that five beverage bottles can be exchanged for one. A class drank 161 bottles of beverage, some of which were left over
If they trade empty bottles for open ones, they should at least buy () bottles
128 bottles
128 = 125 + 3 (25 for 125, 5 for 25, 1 for 5, 1 for 1 Plus + 3 = 4, only one bottle can be replaced. After drinking, add the last empty bottle to just 5)
129 bottles
128 is wrong. If you buy 125 bottles and actually drink 125 2551 yuan, it is equivalent to drinking 156 bottles and drinking 159 bottles in an empty bottle. If you change four bottles for one, it's only 160 bottles. So you can only buy 129 bottles and the remaining one is not good at math. Please give me some advice
121. Process: buy five bottles first, you can get one bottle, and then buy four bottles, you can get another bottle. That is to say, if you buy every four bottles, you can buy x times. Formula: 5 + 4x = 161 x = 39, that is, 39 bottles have been changed. 161-39=122 122-1=121
Given that {an} is an equal ratio sequence, and A4 + A7 = 2, a5a6 = - 8, then a1 + A10 = ()
A. 5B. -5C. 7D. -7
When A4 = 4, a7 = - 2, a7 = 4, when A4 = 4, a7 = - 2, a7 = 4, when A4 = 4, a7 = - 2, Q3 = - 12, A1 = - 8, A10 = 1, a1 + A10 = - 7, when A4 = - 2, a7 = 4, Q3 = - 2, A1 = 1, a1 + A10 = - 7, when A4 = - 2, a7 = 4, Q3 = - 2, then A10 = - 8, A1 = 1, a1 + A10 = - 7
The equal ratio sequence A5 * A6 = A4 * A7 is solved to get A4 A7, and the a1a10 of the equal ratio sequence is solved??? A5a6 = a4a7? How did you get it?
If you subtract 3.6 from a number, 5 times the difference is exactly 3 times the number
Let this number be X. according to the meaning of the question, we can get: (x-3.6) × 5 = 3x, & nbsp; & nbsp; 5x-3.6 × 5 = 3x, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 5x-3x = 3.6 × 5, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 2x = 18, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp
A kind of beverage bottle, whose body is cylindrical (excluding bottle neck). It is known that 540 ml of beverage is contained in the bottle. When the bottle is placed upright, the height of the beverage in the bottle is 18 cm, and when the bottle is placed upside down, the height of the spare part in the bottle is 6 cm. What is the volume of this kind of beverage bottle?
Let the bottom area of the bottle be X
18x = 540-6x (equal beverage volume)
The solution is x = 22.5
5 x 18 = 405 ml
In the equal ratio sequence {an}, A1 = 2, A4 = 16, let BN = 1 / {log2 (an). Log2 [a (n + 1)]}
To prove the first n terms and Sn of sequence {BN}
a4/a1=q³=8
Q=2
∴an=2×2^(n-1)=2^n
∴bn=1/{ log2(2^n) × log2[2^(n+1)] } = 1/ [n(n+1)]
∵bn=1/ [n(n+1)]= 1/n - 1/(n+1)
∴Sn= (1 - 1/2) + (1/2 - 1/3)+ ( 1/3 - 1/4) +…… + [1/n - 1/(n+1) ]
= 1 - 1/(n+1)
=n/(n+1)＜1
3.5 times of the difference of a number minus 6 is exactly equal to 1.1 times of this number
The solution of the equation is based on the equation
Let this number be X
（X-6）×3.5=1.1X
3.5X-21=1.1X
3.5X-1.1X=21
2.4X=21
X=8.75
Let this number be X. according to the meaning of the question, the following equations are listed: (X-6) × 3.5 = 1.1x, 3.5x-21 = 1.1x, 2.4x = 21, x = 8.75)
Let this number be X
3.5(x-6)=1.1x
3.5x-21=1.1x
3.5x-1.1x=21
2.4x=21
24x=210
x=35/4=8.75
Let this number be X
That is, (X-6) * 3.5 = 1.1x
That is, x = 8.75
There are 100 large and small beverage bottles, which just hold 90 kg of beverage. It is known that each large beverage bottle is 1 kg, and each small bottle is 0.75 kg. How many large and small beverage bottles are there?
Better not use equations
Let X and y have small equations
x+y=100
x+0.75y=90
The solution is x = 60, y = 40
--------------------------------
Number of vials: (1 × 100-90) / (1-0.75) = 10 / 0.25 = 40
Number of large bottles: 100-40 = 60
Set X large bottles and Y small bottles
x+y=100
x+0.75y=90
x=60
y=40
There are 60 large bottles and 40 small bottles
It is known that the equal ratio sequence {an} satisfies an > 0, n = 1,2 And A5 * a (2n-5) = 2 ^ 2n, then when n > 1, log2 (A1) + lo
It is known that the equal ratio sequence {an} satisfies an > 0, n = 1,2 And A5 * a (2n-5) = 2 ^ 2n, then when n > 1, log2 (A1) + log2 (A3) + +log2（a（2n-1））=
A5*A（2n-5）=2^(2n)(n≥3)
A1*Q^4 * A1*Q^(2n-6)=2^(2n)
A1^2*Q^(2n-2)=2^(2n)
An=2^n
So log2 (A1) + log2 (A3) + +log2[A（2n-1）]=1+3+…… +(2n-1)=n*2n/2=n²