The general formula of sequence 1,1 / 4,1 / 9,1 / 10 is?

The general formula of sequence 1,1 / 4,1 / 9,1 / 10 is?

1 / N ^ 2n 1 / 2

A general formula of sequence (2 ^ 2-1) / 2, (3 ^ 2-1) / 5, (4 ^ 2-1) / 8, (5 ^ 2-1) / 11

2^2-1=1*3 3^2-1=2*4 4^2-1=3*5 5^2-1=4*6
2=3-1 5=2+3=2*3-1 8=5+3=2+2*3=3*3-1 11=8+3=5+2*3=2+3*3=4*3-1
So the general formula is n * (n + 2) / (3n-1)

Sequence 1,5,18,58. General term formula
There is no hard work, you masters

a1=1
a2=5=1*3+2
a3=18=5*3+3
a4=58=18*3+4
...
an=3an-1+n=3[3a(n-2)+n]+n=3^2a(n-2)+n+3n
=3^2[3a(n-3)+n]+n+3n=3^3a(n-3)+n+3n+3^2n
=...
=3^(n-1)a1+[1+3+3^2+...+3^(n-2)]n
=3^(n-1)+[3^(n-1)-1]n/2
=[(n+2)3^n-3n]/6
The general formula is an = [(n + 2) 3 ^ n-3n] / 6

2,5,9,13,19 and so on. What is the general formula of this series
If it's OK, you'll get extra points··

Fibonacci sequence, such a famous sequence do not know! Use the characteristic equation method plus undetermined coefficient method! Solution: let an - α a (n-1) = β (a (n-1) - α a (n-2)) get α + β = 1, α β = - 1, construct the equation x & sup2; - X-1 = 0, get α = (1 - √ 5) / 2, β = (1 + √ 5) / 2 or α = (1 + √ 5) / 2, β = (1 - √ 5) / 2

General term formula of sequence-1,2, - 5,8 ·

Because it's positive and negative
You can put forward (- 1) ^ n first
Then an = {1,2,5,8 }
When n = 1, A1 = 1
When n > 1, the sequence is equal difference sequence
The second term is 2 and the equal difference is 3
an=2+3*（n-2）=3n-4
So the general term formula of the whole sequence is
An = - 1 (when n = 1)
An = (- 1) ^ n * (3n-4) (when n > 1)

A1 = 3, A2 = 8, A3 = 13, A4 = 18, what is the general formula

In this problem, a2-a1 = 5, a3-a2 = 5, so it can be judged as an arithmetic sequence. We can set the general formula of arithmetic sequence: an = a1 + (n-1)

Find the general formula of 2 / 3, 4 / 18, 6 / 35, 8 / 63, 10 / / 99

The second one should be 4 / 15. The general term is 2n / (2n-1) (2n + 1)

The general formula of 3,9,18,30
fast

The difference between 3 and 9 is 6, which is twice of 3
The difference between 9 and 18 is 9, which is three times of 3
The difference between 18 and 30 is 12, which is 4 times of 3
So let 3, 9, 18 and 30 be A1, A2, A3 and A4 respectively,
Then there are: a2-a1 = 2A1; a3-a2 = 3A1; a4-a3 = 4A1 (the number after a is the corner mark)
By analogy, the general formula is: an-a (n-1) = n A1 (n before A1 is a multiple, which has the same value as the subscript n of an)

Compulsory formula of five general terms, 1,2,3,4,5,6,7 (n-1) general term formula
Seek: 1,2,3,4,5,6,7 The general formula of (n-1) should have a detailed process,
I'm sorry. It's adding them up

It's the general formula of sum
Sn-1 = 1 + 2 + 3 +... + (n-2) + (n-1). (1) formula
Sn-1 = (n-1) + (n-2) +... + 3 + 2 + 1. (2)
The sum of the two formulas leads to
2sn-1 = n + N +... + N + n (n-1 n added)
2Sn-1=n（n-1）
Sn-1=n（n-1）/2

2 8 18 32 50 general term formula

Let A1 = 2, A2 = 8, A3 = 18, A4 = 32, A5 = 50
a2-a1=8-2=6
a3-a2=18-8=10
a4-a3=14
a5-a4=18
Then let B1 = 6, B2 = 10, B3 = 14, B4 = 18
It is known that this sequence is an arithmetic sequence with a tolerance of 4
So sn-1 (b) = B1 + B2 +. + bn-1 = B1 (n-1) + [(n-1) (n-2) * 4] / 2 = 6 (n-1)) + [(n-1) (n-2) * 4] / 2 = 2n ^ 2-2
Then, you should know that the left side of the above formula = a2-a1 + a3-a2 +. + an-a (n-1) = an-a1 = sn-1 (b) = 2n ^ 2-2
That is: an = 2n ^ 2-2 + A1 = 2n ^ 2-2 + 2 = 2n ^ 2
This is the general formula of this sequence: an = 2n ^ 2
I don't know if you understand it. I haven't done it for a long time. I don't know how to express it clearly,