Observe the sequence and complete it: 1, 3, 8, 22, 60______ ，448．

(22 + 60) × 2 = 164, so the answer is: 164

Sequence 106, 0, 1, 3, 8, 22, 64, ()
106、0,1,3,8,22,64,（）
A、174；B、183；C、185；D、190；
107、2,90,46,68,57,（）
A．65；B．62．5；C．63；D．62
108、2,2,0,7,9,9,( )
A．13；B．12；C．18；D．17；
109、 3,8,11,20,71,（）
A．168；B．233；C．211；D．304
110、-1,0,31,80,63,( ),5
A．35；B．24；C．26；D．37；

106. Choose D, 190 8 = [0 + 1 + 3] * 2-0 22 = [0 + 1 + 3 + 8] * 2-2 64 = [0 + 1 + 3 + 8 + 22] * 2-4, so you can get the answer D 190 = [0 + 1 + 3 + 8 + 22 + 64] * 2-6 107. Choose B, 62.5 (2 + 90) △ 2 = 46, 90 + 46) △ 2 = 68 68 + 57) △ 2 = 62.5108

1, 3, 8, 22, 60, (), 48. What should be filled in brackets

1,3,8,22,60,（164）448
1,3 increased by 2
3,8 increased by 5
8,22 increase (2 + 5) * 2 = 14
22,60 increased (5 + 14) * 2 = 38
60, () increased (14 + 38) * 2 = 104
(), 448 increased (104 + 38) * 2 = 284

Observe a column of numbers; 2,4,6,8,10___ (2) according to this rule, if a n (n)
(1) The difference between each number and the previous one is certain, and the difference is_ ；
(2) According to this rule, if a n (n is a positive integer) represents the nth item of the column, then A8= ;
(3) If the value of 2 + 4 + 6 + 8 + 10 +... + 20 is required, we can make s = 2 + 4 + 6 + 8 + 10... + 20. ① arrange the addends of ① from large to small, and we can get s = 20 + 18 + 16 + 14 + 12 +... + 2, ②
① + 2, get 2S=_____ ,
So s = --
The key to solve the problem flexibly is to read the meaning of the question carefully, find out the law of change between two adjacent numbers, and understand the solution provided in the question

(1) The difference between each number and the previous one is 2;
(2) According to this rule, if a n (n is a positive integer) represents the nth item of the column, then A8 = 16
(3) If the value of 2 + 4 + 6 + 8 + 10 +... + 20 is required, we can make s = 2 + 4 + 6 + 8 + 10... + 20. ① arrange the addends of ① from large to small, and we can get s = 20 + 18 + 16 + 14 + 12 +... + 2, ②
① + 2, 2S = 22 × 10 = 220
So s = 220 △ 2 = 110

Please answer the questions of mathematics sequence in senior one in detail, thank you! (209:17:17)
The power function f (x) = x square (m2-2m-3), m ∈ 2, is even function, and decreases on (0, + ∝)
Find f (x)

First find the range of M, you can find - 1

Find the law of mathematical sequence
2,7,23,73227. I have found 2 * 3 + 2 ^ 0 = 7
73+2^1=23
233+2^2=73
73*3+2^3=227
Finding a formula with n only

As you found out: a [n] = 3A [n-1] + 2 ^ (n-2)
A [n] + 2 ^ (n-1) = 3 (a [n-1] + 2 ^ (n-2)) (x, y in a [n] + x2 ^ n = y (a [n-1] + Y2 ^ (n-1)) can be obtained by undetermined coefficient)
Let B [n] = a [n] + 2 ^ (n-1), B [1] = 3, then B [n] is an equal ratio sequence with 3 as the first term and 3 as the common ratio
∴b[n]=a[n]+2^(n-1)=3^n
∴a[n]=3^n-2^(n-1)

(26 14:36:51)
A1 = a + (1 / 4) & # 160; & # 160; & # 160;, & # 160; when an + 1 = (1 / 2) an & # 160; & # 160;, n is even. When an + 1 = an + (1 / 4) & # 160; & # 160;, n is odd
Let BN = a2n-1 · (- 1 / 4), &# 160; n = 1.2.3
1、 Find A2, A3
2、 Judge whether {BN} is an equal ratio sequence

(1)A2=1/2A1=A/2
A3=A2+1/4=(2A+1)/4
(2)B1=A1-1/4=A-1/4≠0
Bn=A2n-1 - 1/4
Bn+1=A2(n+1)-1 - 1/4=A2n+1 - 1/4
A2n+1=1/2A2n
A2n=A2n-1+1=A2n-1 + 1/4
∴ A2n+1 = 1/2(A2n-1 + 1/4)
∴ Bn+1 =1/2(A2n-1 - 1/4)
And BN = a2n-1 - 1 / 4
∴ Bn+1 / Bn =1/2
And B1 ≠ 0
The BN is an equal ratio sequence

The problem of finding the law of sequence
5,8,9,0,-25,-72,（）
[hope to write the general term formula and the process of finding the general term formula (undetermined coefficient?)

-147
Item 1: 2 ^ 2 + 1 ^ 3,
From item 2: (2n) ^ 2 - n ^ 3,
14^2 -7^3=-147

Sequence (160:36:31)
Let f (x) = 1 / 2 ^ x + radical 2, find the value of F (- 5) + F (- 4) +... + F (0) +... + F (6)

Find f (x) + F (1-x) f (x) = 1 / (2 ^ x + √ 2) f (1-x) = 1 / [2 ^ (1-x) + √ 2]. (multiply the numerator and denominator by 2 ^ x) = 2 ^ X / (2 + √ 2 * 2 ^ x). (extract √ 2 from the denominator) = (2 ^ X / √ 2) * (1 / √ 2 + 2 ^ x) = (2 ^ X / √ 2) * f (x) f (x) + F (1-x) = (1 +

Junior high school mathematics to find the law problem = = how to calculate the total increase in the number sequence
Sequence: 2, 5, 10, 17 Find the nth digit
Analysis: the increment of sequence is 3, 5 and 7 respectively, and the increment is increased by the same amplitude. Then, the increment from the n-1st to the n-th digit of sequence is 3 + 2 × (n-2) = 2N-1, and the total increment is:
〔3+（2n-1）〕×(n-1)÷2＝（n+1）×(n-1)＝n2-1
So the nth digit is: 2 + n2-1 = N2 + 1
What is the meaning of [3 + (2n-1)] × (n-1) △ 2?

LZ, where are you doing? This is not the sum of arithmetic series in high school
If the increment of a sequence is an arithmetic sequence (that is, a sequence with equal increments), then the sequence is a quadratic function; if the increment of a sequence is an arithmetic sequence, then the sequence is a cubic function By analogy, this is the knowledge of series
As for the subject,
5-2=3
10-5=5
17-10=7
……
an-a(n-1)=2n-1
An (for the nth bit)
These formulas are added left and right
We can get An-2 = 3 + 5 + 7 + +2n-1
Let t = 3 + 5 + 7 + +2N-1, obviously t is the total increase
By the way, I'll tell you about Gauss algorithm. After all, this topic shouldn't be in junior high school
3+5+7+…… +2N-1 can also be written as
2n-1+2n-3+2n-5+…… +3 (reverse)
Then the items are added, and the sum of the items is the same number 3 + 2N-1, that is, the sum of the first and last items
So 2T = (3 + 2n-1) (n-1)
N-1 is the total number of terms of T
So the total increase t = [3 + (2n - 1)] × (n - 1) △ 2, that's how it comes

Observe the sequence and complete it: 1, 3, 8, 22, 60______ ，448．