Respuesta :
That would be 25,21,17,13...
this is arithmetic with a common difference of -4.
this is arithmetic with a common difference of -4.
Answer:
The correct option is 3.
Step-by-step explanation:
The sequence is called an arithmetic sequence if the difference between every two consecutive terms are same.
In sequence 1, 5, 8, 13, ...
[tex]d_1=a_2-a_1=5-1=4[/tex]
[tex]d_2=a_3-a_2=8-5=3[/tex]
Since [tex]d_1\neq d_2[/tex], therefore the sequence 1, 5, 8, 13, ... is not an arithmetic sequence.
In sequence 2, 4, 8, 32,...
[tex]d_1=a_2-a_1=4-2=2[/tex]
[tex]d_2=a_3-a_2=8-4=4[/tex]
Since [tex]d_1\neq d_2[/tex], therefore the sequence 2, 4, 8, 32,... is not an arithmetic sequence.
In sequence 25, 21, 17, 13, ...
[tex]d_1=a_2-a_1=21-25=-4[/tex]
[tex]d_2=a_3-a_2=17-21=-4[/tex]
[tex]d_3=a_4-a_3=13-17=-4[/tex]
Since this sequence has common difference of -4 therefore the sequence 25, 21, 17, 13, ... is an arithmetic sequence.
In sequence 81, 27, 9, 3, ...
[tex]d_1=a_2-a_1=27-81=-54[/tex]
[tex]d_2=a_3-a_2=9-27=-18[/tex]
Since [tex]d_1\neq d_2[/tex], therefore the sequence 81, 27, 9, 3, ... is not an arithmetic sequence.
Hence the correct option is 3.
