[mathematics] please find out the rules in this series and fill in the blanks 6,1/2,12,1/24,（） Options: A,36 B,72 C,164 D,288 Please give your reasons for choosing this answer,

Choose D
6 divided by 1 / 2 = 12
1 / 2 divided by 12 = 1 / 24
12 divided by 1 / 24 = 288
……

Find out the law of the following sequence and fill in the blanks
（1）：-3,+6,-12,+24,,… (the nth number)
（2）：2,7,12,17,,… (the nth number)
（3）：1,4,9,16,25,,… (the nth number)

The n-th power of the first (- 1) times the N-1 power of 3 times 2
Second 5n-3
The square of the third n

Observe the following sequence, find out the rules and fill in the blanks
1,2,-3,-4,5,6,-7,-8,9,10,-11,-12,… , (1000th) , (2009)

Every four items change positive, + + - -
1000/4=250
-1000
2009 / 4 = 502 + 1
two thousand and nine

The difference between the second and fourth terms of the arithmetic sequence {a (subscript n)} is 6, and the product of the first and fifth terms is - 32

It is known that a2-a4 = - 2D (D is tolerance) = 6, so d = - 3
Then A1 * A5 = - 32, A1 (a1-12) = - 32 can be obtained
Namely: A1 ^ 2-12a1 = 32 = 0
The solution is A1 = 8 or A1 = 4
So the first three terms of the sequence are 8,5,2 or 4,1, - 2

What is the sequence of 3,4,6,12,36? What is the world of 346236

Let an = {3,4,6,23,36,...};
Let BN = an + 1-an;
B1 = a2-a1 = 1;
b2=a3-a2=2;
b3=a4-a3=6;
b4=a5-a4=24;
Observations
bn=n bn;
From this we can draw a conclusion
bn-1=(n-1)bn-2;
.
b2=2b1;
It's very tiring
bn=n!b1=n!;
That is n! = an + 1-an;
n-1!=an-an-1;
.
1!=a2-a1;
An-a1 = 1! + 2! +... + (n-1)! (n > 0);
So: an = 3 + 1! +... + (n-1)!;

History of sequence development

The number sequence of equal proportion originated from some practical problems in ancient times. The king raaus of ancient Egypt had a competent clerical Amos. He wrote a Book of arithmetic in hieroglyphics, which recorded some achievements of mathematical research from 2000 BC to 1700 BC. Among them, there was such a question, in which a ladder was drawn, and the notes at all levels were 7,493432401, 16807. Besides the number, he drew man, cat, mouse, barley and measuring instrument. There was no explanation in the original book, so it became a puzzle in the history of mathematics. No one could explain it for more than 2000 years
Until the middle ages, Fibonacci published the abacus in 1202
Today, seven old women are going to Rome together. Each of them has seven mules. Each mule carries seven bags of bread. Each bag contains seven knives. Each knife is equipped with seven scabbards. How many are all the things listed?
Obviously, this is a summation problem of equal ratio sequence
The original meaning of the Amos problem is: there are seven people, each with seven cats, each cat eats seven rats, each rat eats seven ears of barley, each ear can grow into seven measuring devices of barley. Of course, this is only speculation
Ancient Chinese mathematicians have studied the problem of equal ratio sequence for a long time
Today, there are nine dikes. There are nine trees on the dikes, nine branches on the trees, nine nests on the branches, nine birds on the nests, nine chicks on the birds, nine hairs on the vines and nine colors on the hairs. How many are they?
This is not purely copying each other, but reflects the internal law of mathematical development
This page contains a lot of details. Let's have a look
I have pasted the most difficult development history. Let's figure out the rest

Find the sum of sequence
1/S1+1/S2+1/S3+```````+1/Sn
Value of
I know Sn = n ^ 2 + 2n
How to ask

Sn＝n^2+2n
1/Sn=1/(n^2+2n)=1/n(n+2)=1/2*[1/n-1/(n+2)]
1/S1+1/S2+1/S3+```````+1/Sn=1/2×[(1-1/3)+(1/2-1/4)+(1/3-1/5)+(1/4-1/6)+… +1/n-1/(n+2)]
=1/2×[1+1/2-1/(n+1)-1/(n+2)]
=3/4-(2n+3)/[2(n+1)(n+2)]

Sequence 1 / 2, 1 / 3, 1 / 10, 1 / 15, 1 / 26, 1 / 35, the 10th number in this sequence

Analysis: look at denominator
2=1^2+1 3=2^2-1
10=3^2+1 15=4^2-1
26=5^2+1 35=6^2-1
So the denominator of the tenth number is 10 ^ 2-1 = 99
Answer: 1 / 99

1 / 2, 1 / 3, 1 / 10, 1 / 15, 1 / 26, 1 / 35. According to this rule, the seventh number is

The numerator is all 1, regardless of the denominator
2=1²+1
3=2²-1
10=3²+1
15=4²-1
26=5²+1
35=6²-1
Therefore, the denominator of the seventh number is 7 & # 178; + 1 = 50, that is, the seventh number is 1 / 50

Find the rule: 1,4,16,39121, () what number to fill in the brackets
The method, process and result are clear. There are 252 256 161 169 alternative answers

The sum of two adjacent numbers is a multiple of 5, so this question should be 169
Among the four options, only 169 + 121 = 290 is a multiple of 5

[mathematics] please find out the rules in this series and fill in the blanks 6,1/2,12,1/24,（） Options: A,36 B,72 C,164 D,288 Please give your reasons for choosing this answer,