Table 3 represents an arithmetic sequence.
Solution:
To find which table represents an arithmetic sequence:
In arithmetic sequence difference of each term is equal.
[tex]d=a_n-a_{n-1}[/tex]
Table 1:
[tex]d=a_2-a_1[/tex]
= –12 – (–6)
d = –6
[tex]d=a_3-a_2[/tex]
= –24 – (–12)
d = –12
Here differences are not equal.
So table 1 not represents an arithmetic sequence.
Table 2:
[tex]d=a_2-a_1[/tex]
= 9 – 7
d = 2
[tex]d=a_3-a_2[/tex]
= 13 – 9
d = 4
Here differences are not equal.
So table 2 not represents an arithmetic sequence.
Table 3:
[tex]d=a_2-a_1[/tex]
= 7.3 – 8.7
d = –1.4
[tex]d=a_3-a_2[/tex]
= 5.9 – 7.3
d = –1.4
[tex]d=a_4-a_3[/tex]
= 4.5 – 5.9
d = –1.4
[tex]d=a_5-a_4[/tex]
= 3.1 – 4.5
d = –1.4
Here differences are equal.
So table 3 represents an arithmetic sequence.
