Please find the law of these numbers 3,6,10,15,21 What is the Nth I really love math

a2-a1+a3-a2+a4-a3+..an-a(n-1)=3+4+5+6+..n+1)

Removing the same term on the left leaves AN-A1

On the right is the sum of the difference series, the first term 3 tolerance 1, and the sn=(3+n-1)*(n-1) 2 of the first n-1 term is found

First Item + Stub Item) * Number of Items 2

So it's an-a1 =sn=(n+2)(n-1) 2, you're wrong

a2-a1）+（a3-a2）+（a4-a3）+.an-a(n-1)]=3+4+5+6+..n+1)

Because the result of subtracting the former from the latter item increases by one each time.

3+4+5+6+..n+1) She is a series of equal differences. Equations for the difference series.

Remove the parentheses to obtain: an-a1=(3+n+1)(n-1) 2=(n+4)(n-1) 2

Look for the pattern of these numbers: 3, 6, 10, 15, 21....The nth is 3n

To put it simply, it's the difference method

an = （an-an-1)+(an-1 -an-2) +a2-a1)+a1

Why do you think of this, because a problem like this is generally a polynomial of n, at most an exponential of n, and the number of times the polynomial sequence of neighbors are subtracted (this is called differential) will continue to decrease until.

A series of constant numbers, so that a step-by-step sum will find the general term (i.e., recursive).

The exponential formula has a similar law, except that his difference is an equal proportional sequence.

In higher terms, in combinatorics this is called difference, and doing difference multiple times is called high-order difference, also known as high-order difference.

A discrete form of a derivative.

1st number: 1=1

The second number: 3=1+2

The third number: 6 = 1 + 2 + 3

The fourth number: 10 = 1 + 2 + 3 + 4

The fifth number: 15 = 1 + 2 + 3 + 4 + 5

The 6th state disturbance number: 21 = 1 + 2 + 3 + 4 + 5 + 6 It is easy to see that the nth number is:

1+2+3+4+5+.+n-1)+n

1+n)*n/2

To sum up, it can be seen that the nth number is expressed as a brother: (1+n)*n 2

3,6,10,15,21. a2-a1=3, a3-a2=4 a4-a3=5 a5-a4=6 .an-a(n-1)=n+1 The sum of all formulas a2-a1+a3-a2+a4-a3+...

an-a(n-1)=3+4+5+6+..n+1) an-a1=(3+n+1)(n-1) 2=(n+4)(n-1) 2 an=3+(n+4)(n-1) coarse slag sorghum 2

1 + 2 = 3, 3 + 3 = 6, 6 + 4 = 10, 10 + 5 = 15, the number of wax cavities added in turn is added by 1, so it is 15 + 6 = 21. Fill in the auction macro 21.

From item 2 onwards, the difference between each term and the previous term is a natural number elimination column starting with 3.

e.g. 6-3=3;

The formula next to the bridge is an=2n+1+n(n-1) 2 (n=1,2,3,4,5).

So the next potato match is 21, 28 ,......Sell celery....

The law of the socks of the rule:

General formula: n(n+1) 2 (n is a positive integer).

Therefore: it can also be understood as good scum: the interval between the first blind numbers is: 2, 3, 4, 5, 6, 7, 8, 9 in order of increasing order.

The second number is 1 larger than the first number, the third number is 2 larger than the second number, the fourth number is 3 larger than the third number, and so on.

1，3，6，10，15，21，28，36。The latter numbers are 2, 3, 4, 5, 6, 7, and 8 more than the previous ones

0，1，3，6，10，15，21。The latter numbers are 1, 2, 3, 4, 5, and 6 more than the previous ones

Summary. Hello classmates, these numbers, after subtracting each adjacent two numbers, are equal to 4, -8, 16, and -36 respectively, and it can be seen that the difference between them is -2 times.

What is the pattern in the numbers 1, 3, -5, 11, -21?

Hello with the lack of brother Zhenxue, this is a few numbers, after subtracting each adjacent two numbers, the dust hole is equal to 4, -8, 16, -36 It can be seen that the difference between them is -2 times the relationship.

I hope mine can help you

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