Three numbers are equal difference series, and the ratio is 3:4:5. If the minimum number is added with 1, then three numbers will be equal difference series. What are the far three numbers? Urgent. To process

Let the three numbers be: 3A, 4A and 5A respectively
According to the meaning of the title, we can get the following results
(3a + 1), 4a, 5A are equal ratio sequence
The results are as follows:
(4a)^2=5a(3a+1)
16a^2=15a^2+5a
a^2-5a=0
a1=0,a2=5
A = 0 (not conforming, rounding off)
therefore
a=5
3a=15,4a=20,5a=25
These three numbers are: 15, 20, 25

It is known that a, B and C are equal difference sequence, and the tolerance is d (D ≠ 0); C, a and B are equal ratio sequence, and the common ratio is Q, and d = - 6q, so we can find a, B and C

b=a+d
c=a+2d
bc=a^2=(a+d)(a+2d)=a^2=a^2+3ad+2d^2
So 3aD + 2D ^ 2 = 0
And d = - 6q
72q^2=18aq
4q=a
b=4q^2
c=4
And a + 2D = 4
So 4q + 2D = 4
-2q=4
q=-2
So B = 16
a=-8
c=4

Given that a, B and C are equal difference sequence and equal ratio sequence, we can prove a = b = C
I hope I can answer the process. Thank you

From the meaning of the title, we know that B = (a + C) / 2 B ^ 2 = AC, so there is (a + C) ^ 2 = 4ac

It is known that the first three of the four numbers a, B, C and D are equal ratio sequences with 1 / 2 as the common ratio, and the last three are equal difference sequences with - 2 as the tolerance
(1) Find the four numbers a, B, C and D
(2) If a, B, C and D are the first three terms of the equal ratio sequence {an} and the equal difference sequence {BN}, CN = an + 2bn, find the sum of the first n terms of the sequence {CN}
(2) Change: if a, B and C are the first three terms of the equal ratio sequence {an}, B, C and D are the first three terms of the equal difference sequence {BN}, CN = an + 2bn, find the sum of the first n terms of the sequence {CN}

(1) The first three are equal ratio sequences with 1 / 2 as common ratio, so B = 1 / 2 * a ① C = 1 / 2 * B ②
The last three are arithmetic sequences with - 2 as tolerance, so C = B-2 ③ d = C-2 ④
According to formula 2 and 3, B = 4 and C = 2 can be obtained
Substituting into formula (1) and (4), we can get a = 8 and d = 0
(2) If a, B, C and D are equal ratio sequence and {an} is equal difference sequence, the first three terms of {BN} are not understood

The three positive numbers a, B, C form the arithmetic sequence, C-A, B, C + a form the arithmetic sequence, find a: B: C

a. If B and C are equal, then a + C = 2B （1）
Then (C-A) (c + a) = B ^ 2 （2）
c^2-a^2=b^2
From (1), it is concluded that:
(a+c)^2=4b^2………… （3）
(3) (2)
(a+c)/(c-a)=4
a+c=4c-4a
5a=3c
c=5/3a
Substituting (1) to get:
a+5/3a=2b
8/3a=2b
b=4/3a
therefore
a:b:c
=a:4/3a:5/3a
=3:4:5

360,72,18,6
According to the law

360 (divided by 5) 72 (divided by 4) 18 (divided by 3) 6 (divided by 2) yes
360,72,18,6,(3,1)

3, 3, 6, 18, 72, 360, what's the number after that

2160

3,3,6 ,18 ,72,9 ( ) A.144 B.360 C.540 D.640

You wrote an extra nine
3*1=3
3*2=6
6*3=18
18*4=72
72*5=360
Option B

Observe the following three lines: - 3.9. - 27.81. - 243. - 5.7. - 29.79. - 245
Look at the following three lines:
-3.9.-27.81.-243.
-5.7.-29.79.-245.
1.-3.9.-27.81.
(1) What is the order of the first row?
(2) Second, what is the relationship between the number of the third row and the number of the first row?
(3) Take the sixth number in each row to calculate their sum

(1) Take - 3 every time

The description of {1,3,5,7,9,11} sets

Descriptive method
{x|x=2k-1,1

Three numbers are equal difference series, and the ratio is 3:4:5. If the minimum number is added with 1, then three numbers will be equal difference series. What are the far three numbers? Urgent. To process