ลำดับเลขคณิต [Arithmetic Sequence o

ลำดับเลขคณิต [Arithmetic Sequence or Arithmetic Progression] ย่อด้วย A.P. หรือ A.S.
นิยาม ลำดับเลขคณิต คือ ลำดับซึ่งผลต่างร่วม [Common difference ตัวย่อ d] ระหว่างพจน์ที่ an+1 กับพจน์ที่ an
มีค่าคงที่ สำหรับทุกๆ n
นั้นคือ d = an+1 - an
รูปทั่วๆไปของลำดับเลขคณิต คือ a1 , a1+d , a1+2d , ... , a1+(n-1)d , ...
พจน์ที่ n คือ an = a1+(n-1)d

ตัวอย่าง 1 กำหนดลำดับเลขคณิตมีพจน์ที่ 1 เป็น 7 และผลต่างร่วมเป็น 5 จงหา a8 และ a12
วิธีทำ เพราะว่า a1 = 7 และ d = 5
เพราะฉะนั้น a8 = a1+ 7d = 7 + 7(5) = 42
a12 = a1+ 11d = 7 + 11(5) = 62

ตัวอย่าง 2 จงหาพจน์ที่ 10 และพจน์ที่ 15 ของลำดับเลขคณิต 4, 9, 14, 19, ...
วิธีทำ จากโจทย์ a1 = 4
d = 9 - 4 = 5
a10 = a1 + 9d = 4 + 9(5) = 49
a15 = a1 + 14d = 4 + 14(5) = 74

ผลลัพธ์ (อังกฤษ) 1:

Arithmetic sequences [Arithmetic Progression or Arithmetic Sequence] note. A.P. or the arithmetic sequence definition
A.S. respectively, which shared variance [Common difference d abbreviation] between terms that an an that terms with 1
a
n for every constant is d = 1 an-an
. General image of the sequence is arithmetic a1 a1 a1, d, 2d, ..., a1 (n-1)
n where d is the term ... an = a1 (n-1): d

, for example determining the sequence is arithmetic terms 1 1 is 7 and the difference is 5 you shall find out how to make the a8 and a12
a1 = 7 and the d = 5
7d = a8 = therefore, 7 7 a1 (5) = 42
. A12 = a1 = 7 11d 11 (5) = 62

2, for example, for the terms "10 and that the terms of the sequence, 15 4 9 arithmetic, 14, 19, from a1 problem how to do ... =
4
d = 9-4 = 5
4 = 9d = a1 a10 9 (5) = 14d
a1 49 a15 = 4 = 14 (5) = 74


.

ผลลัพธ์ (อังกฤษ) 2:

Order arithmetic [Arithmetic Sequence or Arithmetic Progression] abbreviated AP or AS.
define an arithmetic sequence is a sequence in which the difference [Common difference abbreviations d] the expression an +1 to the nth term an.
were constant for each n.
then is d = an +1 - an
is basic arithmetic sequence is a1, a1 + d, a1 +2 d, ..., a1 + (n-1) d, ...
, n is the nth term an = a1 + (n-1). d Example 1 Given the arithmetic sequence with nth term 1 is 7, and the difference is 5, find a8 and a12. way because a1 = 7 and d = 5. hence A8 = A1 + 7d = 7 + 7 (5) = 42. A12 = A1 + 11d = 7 + 11 (5) = 62. Example 2 Determine the nth term 10 and term 15 of the arithmetic sequence 4, 9, 14, 19, ... ways of Proposition A1 = 4. D = 9 - 4 = 5. A10 = 9D = A1 + 4 + 9 (5) = 49. A15 = A1 + 14D = 4 + 14 (5) = 74.

ผลลัพธ์ (อังกฤษ) 3:

Arithmetic sequence [Arithmetic Sequence or Arithmetic Progression] out with A.P. Or A.S.
definition of limit of a sequence is a sequence in which the difference of cooperation [Common difference abbreviation D] between the word an 1 with word an
constant for every n
is d = an 1 - an
The general picture of dinosaurs is A1, A1 D, A1 2D,..., A1 (n-1) d,...
word n is an = A1 (n-1) d

examples 1 set sequence arithmetic have word 1 is 7 and the difference in 5 seek A8 A12
and method. Because A1 = and = 7 d 5
so A8 = A1 7d = 7 7 (5) = 42
A12 = A1 11d = 7 11 (5) = 62

examples 2 find the word and the word 10 15 of dinosaurs 4 9 14,,,, 19...
how to do from the problem A1 = 4
D = 9 - 4 = 5
A10 = A1 9D = 4 9 (5) = 49
A15 = A1 14d = 4 14 (5) = 74