arithmetic sequences
An arithmetic sequence is characterized by the fact that successive members all have the same distance d. Each successive member (except the first one) is the arithmetic mean of its neighboring members. From the school time of the important German mathematician Carl Friedrich Gauss (1777 to 1855) the following is handed down:
The teacher, who practiced beekeeping on the side, needed time to catch a swarm of bees. Therefore he set his students of the arithmetic class a task to occupy them long - https://domyhomework.club/ , they should add the numbers from 1 to 100. nine-year-old GAUSS already called out the correct result, 5050.
Gauss had not calculated 1+2+3+... like his classmates - matlab homework help . but simply considered that the sums 100+1, 99+2, 98+3, etc. each add up to 101 and that exactly 50 such pairs of numbers can be formed, resulting in 50⋅101=5050. Thus he had discovered principle in the summation formula of the arithmetic series.
An arithmetic series - accounting homework help - is characterized by the fact that the difference between two adjacent members is always the same, ie, that for all members of the series applies:
an=an-1+d
Examples:
(1) 5; 9; 13; 17; 21; 25; 29 ... d=4
(2) 20; 17; 14; 11; 8; 5 ... d=- 3
(3) 2.1; 2.2; 2,3; 2.4; 2.5; 2.6; 2.7 ... d=0.1
(4) 1; 0.5; 0; -0.5; -1; -1.5; -2 ... d=- 0.5
(5) 6; 6; 6; 6; 6 ... d=0
By specifying the difference d and the initial element a1, the entire sequence is determined, because the following applies:
an=a1+(n-1)d
More information:
Composition and origin of fine dust
