(1) 3, 7, 11, 15, 19, ...
(2) 30, 25, 20, 15, 10,.
Note that the difference between ethnic-tribe is always fixed. Such rows are called ranks arithmetic. The difference is called a different tribe or a different course and is denoted by c.
Rows (l) has a different, b = 4. Front row is called an arithmetic increase because the value of interest-tribe bigger.
Rows (2) has a different, b = -5. Front row is called arithmetic down because the value of the smaller ethnic-tribe.
A line of U1, U2, U3,.... called an arithmetic sequence if the difference of two successive rate is fixed. Value To determine the rate of the n-th row of arithmetic. consider again the example sequence (l).
Let U1, U2, U3, .... is the arithmetic sequence is then
U1 = 3 =+ 4 (0)
U2 = 7 = 3 + 4 = 3 + 4 (1)
U3 = 11 = 3 + 4 + 4 = 3 + 4 (2)
....
Un = 3 + 4(n-1)
In general, if the rate of the first (U1) = a and the sequence is different tribe from the formula b, Un = 3 + 4 (n - 1) obtained 3 is a and 4 is b. Therefore, the interest to-n can be formulated
Un = a + b (n-1)
Rows of arithmetic that have a positive difference is called an arithmetic sequence increased, whereas if a negative difference is called an arithmetic sequence down.
U1, U2, U3, ....... Un-1, Un-called arithmetic progressions, if
U2 - U1 = U3 - U2 = .... = Un - Un-1 = constant
Un = a + (n-1) b = bn + (ab) → Function linear in n
As discussed earlier, the series is a summation of the tribes in a row. If U1, U2, U3, ... arithmetic sequence. U1, U2, U3, ... is the arithmetic series.
To obtain the number n the first tribe of arithmetic series, note the back row of the resulting sequence (l).
3 +7 + 1l + 15 + 19 + ...
If the number of first rate denoted n dengan.Sn the S from the above series are:
Picture: 58.jpg
Note the first tribe of 5 S obtained. Number 3 in the calculation is derived from the first tribe, while the l9 is the tribe of the 5th. Therefore, the amount of interest is the n-th
Picture: 59.jpg
If the value of Un is unknown, we use the formula Un, arithmetic sequence, ie Un = a + (n-1) b, so the first term is the number n
Picture: 60.jpg
n the number of first term of an arithmetic series which first rate a and b are different
Picture: 61.jpg
To facilitate the calculation of Sn an arithmetic series, note the following. a. If the first tribe known a and b different, use the formula Image: 62.jpg b. If the first known tribe and tribe to-n, use the formula Image: 63.jpg
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