Deret Aritmatika: Program Seeking Series Arithmetic and Number Series Arithmetic

Arithmetic series in the field of mathematics is the sequence number in which the next number of additions to the previous number by a number of specific differences. Examples are 3,5,7,9,11,13, ..... Arithmetic series can be expressed with the following formula:

  In this case the n-th quarter:

The total of all quarters:

For example, the total rate of a quarter of the form a_n = 3 + (n-1)(5) up to a quarter-50 is :

Arithmetic series can also be written as follows:

a + (a + b) + (a +2 b) +. . . . . . + (a + (n-1) b)

a = initial rate

b = difference

n = many tribes

U_n = a + (n - 1) b is the n-th quarter

Total n rates :

Sn   = 1 / 2 n (a + Un)
       = 1 / 2 n [2a + (n-1) b]
       = 1/2bn² + (a - 1/2b) n --> quadratic function (in n)

Description:
1. Differences between the two successive quarters is fixed (b = Sn ")
2. Front arithmetic will rise if b> 0
    Front arithmetic will go down if b <0
3. Relationships occur Un = Sn - Sn-1, or Un = Sn '- 1 / 2 Sn "
4. If an odd number of quarter, the central rate
     U_t = ¹ / ₂ (U₁ + U_n) = ¹ / ₂ (U2 + U_n-1)
5. S_n = ¹ / ₂ n (a + U_n) = nU_t  -->  U_t = Sn / n
6. If three numbers form an arithmetic line, so to simplify the calculation of these numbers suppose it is a - b, a, a + b

Procedures for making me make something like this:

For more detailed study of existing programs to try to complete the understanding will be easier. Please download the ziddu. Good work!