1,3,6,10,15,21…… Please write the algebraic expression of item n

3-1=2
6-3=3
10-6=4
15-10=5
21-15=6
.
an-a(n-1)=n
Add the above expressions to get
an-1=2+3+4+...+n
an=1+2+3+...+n
=n(n+1)/2

RELATED INFORMATIONS

1. When n is 1, the algebra is 6, when n is 2, the algebraic formula is 10, when n is 3, the algebra is 15
2. Numbers 1, 3, 6, 10, 15, 21, 28, 36, 45, 55 Can it be expressed in an algebraic expression? Why?
3. Find the rule 3.9.15.21 () ()
4. Please find the law of these numbers: 3,6,10,15,21. What is the nth
5. As shown in the figure, in the triangle ABC, the angle ABC = 30 degrees, take BC and AC as sides, make equilateral △ BCD and equilateral △ ace, and connect be. To prove, AB square + BC square = be square
6. Given vector a = (1,1 / 2), vector b = (0, - 1 / 2), vector C = vector a + k * vector B, vector D = vector a-vector B, the angle between vector C and vector D is π / 4, find the value of real number k in detail
7. It is known that in △ ABC, BD bisects ∠ ABC, ed ‖ BC, EF ‖ AC, and it is proved that be = CF
8. In the parallelogram ABCD, if vector AB + vector ad = vector ab - vector ad, then there must be A vector ad = vector 0 B ABCD is a square C ABCD is a rectangle D vector AB = vector 0 or vector ad = vector 0
9. In the RT triangle ABC, if ∠ C = 90 ° AB = 13 and the radius of the inscribed circle is 2, the perimeter of the triangle ABC is 0 Such as the title
10. Given that the value of y = loga (3a-1) is always positive, then the value range of a is______ ．
11. There is a column of numbers 1.3.6.10.15.21. The nth number is represented by an algebraic expression containing n
12. Observe x ^ - 1, - 2x ^ - 2,4x ^ - 3, - 8x ^ - 4,16x ^ - 5 What do you find? 2. Write the nth formula according to the law. Use a simple process to prove the law you found
13. What is (4x + 5) (4x-5) = 4 (2x + 3) square - (100x-17) 4 (2x + 3) squared is the multiplication of two 4 (2x + 3)
14. (20x^3-8x^2+4x)/( )=5x^2-2x+1
15. (1) X ^ 2-6x + 9 / x ^ 2-4, where x = 3; (2) x ^ 2-4x / x ^ 2-8x + 16, where x = 5
16. x²+4x-2=0,x²-4x+1=0,(x+√5)(x-√5)=20,x²+6x+5=8x+7,25(2x-1)²-16=0,
17. Observe the characteristics of the following monomials: 1 / 2x & # 178; y, - 1 / 4x & # 178; Y & # 178;, 1 / 8x & # 178; Y & # 179;, - 1 / 16x & # 178; y Λ 4 (Λ table) Observe the characteristics of the following monomials: 1 / 2x-178; y, - 1 / 4x-178; y-178;, 1 / 8x-178; y-179;, - 1 / 16x-178; y-4 (Λ denotes power) . (1) Please write the eighth monomial according to this rule. How many times is it? (2) Try to guess: what is the nth monomial? What are its coefficients? How many times?
18. A group of monomials are: - 2x, 4x & # 178;, - 8x & # 179;,... Observe the law, infer that the nth monomials should be - Such as the title
19. What is the second power of - 1 + 5 × (1 / 3 + 1 / 2) × 2012 power of (- 1 / 4) × 2013 power of (- 1 / 4) emergency
20. Square of 1 + 2 + 2 + cubic of 2 +... + 2009 power of 2