Find the sequence 0,1,3,6,10,15,21 The general term formula of

Find the sequence 0,1,3,6,10,15,21 The general term formula of

The second method is to get a (n + 1) = an + N, that is, a (n + 1) - an = n + 1, so a2-a1 + a3-a2 + a4-a3 +... + a (n + 1) - A

Given that the sequence {an} is 6,9,14,21,30, ·· try to find the general term formula of the sequence {an}

a1 = 6
a2 = a1 + 2 * 2 - 1
a3 = a2 + 2 * 3 - 1
a4 = a3 + 2 * 4 - 1
...
an = a(n-1) + 2 * n - 1
The results are as follows
an = 6 + 2 * (2 + 3 + 4 + ... + n) - (n - 1)
= 6 + 2 * (n + 2) * (n - 1) / 2 - (n - 1)
= 6 + (n + 1) * (n - 1)
= n^2 + 5
So:
The general formula of {an} is an = n ^ 2 + 5

What is the general term formula of 1 + 4 + 9 + 16... + N2

Because in your formula: 1 = 1 ^ 2 (a ^ B, which means a to the power of B)
4=2^2
9=3^2
……
Your formula is to accumulate the square of 1 to the square of N. its general formula is as follows:
N (n + 1) (2n + 1)
In addition, let me tell you one more. There is also a general formula of adding the cubic power of 1 to the cubic power of n
Add the sum of N from 1, then square it, that is: [n / 2 (n + 1)] ^ 2

What is the general formula of 9 73 585 4681?

An=1+8An-1

Sequence 1,1-3 + 9,1-3 + 9-27 The general formula of is?
Hope the master can give a certain answer steps and explanation. Thank you.

1,1-3+9,1-3+9-27+81,…
One number for the first term, three numbers for the second term, five numbers for the third term The sum of (2n-1) numbers in the nth term
The (2n-1) numbers form the sum of the equal ratio sequence with the first term of 1 and the common ratio of - 3
So the general formula is 1-3 + 9-27 + 81 + =（1-（-3）^(2n-1))/(1+3)
=（1-（-3）^(2n-1))/4.

According to the first five terms of the following infinite sequence, write out a general term formula of the sequence. (1) 4, 9, 16, 25, 36

an=(n+1)^2

According to the first five terms of the following infinite sequence, write a general formula of the sequence: 1. 2,2,2,2 ⑵ 4,9,16,25,36,…

(i)
2,2,2,2,2...
an =2
(ii)
4,9,16
an = (n+1)^2

Find 1 / 3,1,9 / 5,8 / 3 The general term formula of

1/3 4/4 9/5 16/6.
n^2/n+2

A general formula of sequence 1,1,5 / 7,7 / 15,9 / 31,... Is

1/1,3/3,5/7,7/15,9/31
The molecular weight is 2N-1
The denominator is (2 ^ n) - 1
an=(2n-1)/[(2^n)-1]

Write a general formula of the following sequence, 1, - 3,5, - 7,9

(2N-1)*(-1)^(N+1)