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Given the line segment AB, take a point C on the extension line of AB so that BC = 3AB, take a point D on the extension line of Ba so that Da = 32ab, e is the midpoint of DB, and EB = 30cm, and calculate the length of DC
As shown in the figure: ∵ Da = 32ab, e is the midpoint of DB, ∵ be = 54ab, be = 30cm, ∵ AB = 24cm, ∵ DC = BD + BC = 52ab + 3AB = 132cm
Given the line segment AB, take a point C on the extension line of AB so that BC = 3AB, take a point D on the extension line of Ba so that Da = 32ab, e is the midpoint of DB, and EB = 30cm, and calculate the length of DC
As shown in the figure: ∵ Da = 32ab, e is the midpoint of DB, ∵ be = 54ab, be = 30cm, ∵ AB = 24cm, ∵ DC = BD + BC = 52ab + 3AB = 132cm
It is known that the line segment AB = 10cm, C is a point on the extension line of AB, M is the midpoint of the line segment AC, n is the midpoint of the line segment BC, and Mn is the line segment=______ ．
∵ point m is the midpoint of AC, ∵ MC = 12ac, ∵ point n is the midpoint of BC, ∵ CN = 12bc, Mn = mc-cn = 12 (ac-bc) = 12ab = 12 × 10 = 5
It is known that the sequence {an} is an equal ratio sequence with positive items, A3 = 4, and the sum of the first three terms of {an} is equal to 7
(1) Find the general term formula of sequence {an} (2) if A1B1 + a2b2 + +Anbn = (2n-3) 2 ^ n + 3, let the sum of the first n terms of the sequence (BN) be Sn, and prove: 1 / S1 + 1 / S2 + +1/Sn
(1) Given A3 = 4, S3 = a1 + A2 + a3 --- > a1 + A2 = 7-4 = 3a2 * A2 = A1 * A3 --- > 4A1 = A2 * A2, A2 = 2 or a = - 6 can be obtained from 1.2. Given that the sequence {an} is an equal ratio sequence of positive numbers, A2 = 2, q = 2, A1 = 1An = 2 ^ (n-1); (2) given A1B1 + a2b2 + +anbn=(2n-3)2^...
In the equal ratio sequence [an], A2 equals 2 and A3 equals 4
∵ {an} is an equal ratio sequence
∴a2q=a3
That is, the common ratio q = A3 / A2 = 2
First term A1 = A2 / Q = 1
Then the general formula of sequence {an} is: an = a1q ^ (n-1) = 2 ^ (n-1), n = 1,2,3
^For example, a ^ 5 is the fifth power of A
In the equal ratio sequence an, the general term formula of an is obtained by knowing that A2 is equal to 2 and A3 is equal to 4
Common ratio = A3 / A2 = 2, an = C2 ^ n
n=2,a2=c*2^2=2,c=1/2
an=2^(n-1)
It is known that the sequence an is an equal ratio sequence with positive items, and A1 is equal to 1, A2 plus A3 is equal to 6. Find (1) the general term formula of the sequence an, and (2) the sum of the first ten terms of the sequence S10
Let the common ratio be q, then A2 = q, A3 = q ^ 2. So Q + Q ^ 2 = 6. If Q > 0, then the solution is q = 2. So an = 2 ^ (n-1). From the previous n terms and formula, S10 = A1 (1-Q ^ n) / (1-Q) = 2 ^ 10-1
It is known that A1 plus A3 is equal to 10 in the equal ratio sequence {an}, and the sum of the first four terms is 40. The general term formula of the sequence {an} is obtained
Equal ratio sequence
an=a1q^(n-1)
a3=a1q^2 a1+a3=10 a1+a1q^2=10
A1 (1 + Q ^ 2) = 10 (1)
a1+a2+a3+a4=40 a2+a4=30 a1q+a1q^3=30
Equation a1q (1 + Q ^ 2) = 30 (2)
(2) (1) q = 3
Substituting q = 3 into (1) yields A1 = 1
General term an = 3 ^ (n-1)
It is known that the sum of the first three terms of {an} is equal to 7, and the product is equal to 8. The general term formula of this sequence is obtained
Let the first term be A1 and the common ratio be Q. from the known result, a1 + A1 * q + A1 * q ^ 2 = 7 A1 * A1 * q ^ * A1 * q ^ 2 = 8, so (A1 * q) ^ 3 = 8 A1 * q = 2 q = 2 / A1 A1 a1 + A1 * q + A1 * q ^ 2 = 7 a1 + 2 + 4 / A1 = 7 A1 ^ 2 + 2A1 + 4 = 7a1
The solution of A1 ^ 2-5a1 + 4 = 0 (A1-1) (a1-4) = 0 is A1 = 1 or, A1 = 4, A1 = 1, q = 2, A1 = 4, q = 1 / 2
So an = A1 * q (^ n-1) = 2 ^ (n-1) or an = A1 * q (^ n-1) = 2 ^ (3-N)
It is known that all items of the equal ratio sequence {an} are positive numbers, A1 = 2, and the sum of the first three items is 14. (1) find the general formula of {an}. (2) let BN = log2an, find the sum of the first 20 items of the sequence {BN}
(1) It is known that: a1 + A2 + a3 = 14, that is: a1 + a1q + a1q2 = 14, 2 + 2q + 2q2 = 14, each of the solutions: q = 2, or q = - 3 ∵ {an} is a positive number, q = - 3 is rounded off, an = a1qn-1 = 2 × 2N-1 = 2n, (2) ∵ BN = log2an = n, and {BN} is an arithmetic sequence with 1 as the first term and tolerance of 1, S20 = 20 × 1 + 20 ×
RELATED INFORMATIONS
- 1. Given the line AB = 10cm, C is on the line AB, M is the midpoint of AC, n is the midpoint of BC, 1. When C is on the line AB, find Mn 2. When C is on the extension of Ba Finding the length of Mn
- 2. As shown in the figure, it is known that M is the midpoint of AB and N is the midpoint of AC. if Mn = 5cm, then BC=______ cm．
- 3. If D is the midpoint of AB, then the length of DC is 10 cm, right
- 4. It is known that there is a point C on the line AB, M is the midpoint of AC, n is the midpoint of BC, ab = 12 cm. Please draw a figure according to the title and find out the length of Mn Please write down the process clearly, thank you
- 5. Line BD = 1 / 3AB = 1 / 4CD, points m and N are the middle points of line AB and CD respectively, and Mn = 20cm, find the length of AC A -- m -- D -- B -- N -- C
- 6. As shown in Figure 7, given the common part BC = 1 / 3AB = 1 / 4CD of line AB and CD, the midpoint of line AB and CD are m and N respectively, and Mn = 10cm, find the common part of line AB and CD
- 7. As shown in the figure, the line AB = 8 cm, m and N are the midpoint of BC and AC respectively, then what is the length of Mn, On the same plane
- 8. As shown in the figure, point C is a point on line AB, m and N are the midpoint of line AC and CB respectively. Given AB = 10, find the length of Mn Question 2: as shown in the figure, point C is a point on line AB, and m and N are the midpoint of line AC and CB respectively. Given AB = α, find the length of Mn
- 9. As shown in the figure, B and C divide the line segment ad into three parts, the ratio is ab: BC: CD = 2:3:4, M is the midpoint of the line segment ad, CM = 1cm, find the length of the line segment AD and the value of CM: CD Don't copy it!
- 10. It is known that: as shown in Figure 1, M is a certain point on the fixed length line AB, C and D respectively start from m and B and move to the left along the straight line BA at the speed of 1cm / s and 3cm / s, and the direction of motion is shown by the arrow (C is on the line am, D is on the line BM) (1) If AB = 10cm, when points c and d move for 2S, find the value of AC + MD. (2) if points c and d move, there is always MD = 3aC, fill in the blank directly: am=______ Ab. (3) under the condition of (2), where n is a point on the line AB and an-bn = Mn, the value of mnab is obtained
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