Write 4, 7, 11, 16, 22, 29 The general term formula of,

Write 4, 7, 11, 16, 22, 29 The general term formula of,

The difference between the latter and the former is 3,4,5,6,7
So this is a second-order arithmetic sequence,
Let an = PN ^ 2 + QN + R,
Let n = 1 get P + Q + r = 4, let n = 2 get 4P + 2q + r = 7, let n = 3 get 9p + 3Q + r = 11,
The solution is p = 1 / 2, q = 3 / 2, r = 2,
Therefore, the general term of sequence is an = 1 / 2 * (n ^ 2 + 3N + 4)

General term formula of 1.2.4.7.11.16.22

1 + 1=2
2 + 2=4
4 + 3=7
7 + 4=11
11+ 5=16
16+ 6=22
22+ 7=29
A (n-1) + (n-1) = a n
an-a1 = 1+2+3+4+...+(n-1)=1/2 *n*(n-1)
an = 1/2 *n*(n-1) +1

Fill in 1,2,4,7 (), 22,29, (), 46 1,2,4,11，（），22，29，（），46

It should be 1,2,4,7 (), (), 22,29, (), 46
2-1＝1
4-2＝2
7-4＝3
1,2,4,7 （11）,（16）22,29,（37）,46

What is the law of numbers 1,2,4,7,11,16,22,29? Write formulas in letters

1 + (1) = 22 + (2) = 44 + (3) = 7 7 7 + (4) = 11 11 11 + (5) = 16

Find the rule: - 1, - 2,1, - 3,4, - 7,11, - 18,29. What is the next number? Why? Please explain the reason

-47,
From the third number, each is equal to the difference between the two numbers before it, and the first two minus the first one
The general formula is an = An-2 - an-1

Find the rule and fill in - 12 - 510 - 17, and find the number of 2009 The one with (-) in front is negative. Please tell me the law. (I know the law of the first few numbers, but I don't know how to find the 2009 number.) thank you very much_ ∩)o

The general term is
(-1)^n*[1+(n-1)^2]
In a nutshell:
Exclude positive and negative first
The first term is the square of 1 + 0
The second term is the square of 1 + 1
The third term is the square of 1 + 2
The fourth term is the square of 1 + 3
So item 2009 is the square of 1 + 2008, which is 4032065
Plus plus minus
So it's - 4032065

1 1 / 2 6 / 11 17 / 29 23 / 38

It was divided into 1 / 1, 2 / 4, 6 / 11, 17 / 29, 46 / 76
The numerator of the second term is the numerator + denominator of the former fraction, and the denominator is the denominator of the former term + its own numerator + 1

1, 1 / 2, 16 / 11, 17 / 29 and 23 / 38, respectively

The sum of the denominator of the former term is equal to the numerator of the next term, i.e. 1 + 1 = 22 + 4 = 66 + 17 = 2317 + 29 = 4676 + 46 = 122, the sum of the former denominator and the latter numerator plus 1 equals the denominator of the latter term, i.e. 1 + 2 + 1 = 44 + 6 + 1 = 1111 + 17 + 1 = 2929 + 46 + 1 = 7676 + 122

1. Finding rules: 3,2,11,14, (), 34 2, finding rules: 1,1 / 2,6 / 11,17 / 29,23 / 38, ()

1、11-3=8
14-2=12
( )-11=16 ( )=27
34-14=20
8, 12, 16, 20 are all four
2. The original formula is changed into: 1 / 1, 2 / 4, 6 / 11, 17 / 29, 46 / 76
It can be seen that the numerator of the second term is the numerator + denominator of the former fraction, and the denominator is the denominator of the former term + its own numerator + 1
So the answer is: 122 / 199

Fill in 1,1 / 2,6 / 11,17 / 29,23 / 38 according to the rule to find the next number

The original formula is changed into: 1 / 1, 2 / 4, 6 / 11, 17 / 29, 46 / 76,
It can be seen that the numerator of the second term is the numerator + denominator of the previous fraction,
The denominator is the denominator of the previous term + its own molecule + 1;
The answer is: 122 / 199