Answer:
The arithmetic sequence is: Option: D
D. 3,6,9,12,15
Step-by-step explanation:
We know that a sequence is an arithmetic sequence if each of the term of the sequence exceeds it's preceding sequence by a constant term which is known as a common difference of a sequence.
A)
1,4,5,9,14
Now we calculate the difference between the terms as:
[tex]4-1=3\\\\5-4=1\\\\9-5=4\\\\14-9=5[/tex]
As the difference is not same.
Hence, option: A is not an arithmetic sequence.
B)
6,13,19,32,51
The difference is calculated as:
[tex]13-6=7\\\\19-13=6\\\\32-19=13\\\\51-32=19[/tex]
As the difference is not same.
Hence, option: B is not an arithmetic sequence.
C)
3,5,8,13,21
The difference is calculated as:
[tex]5-3=2\\\\8-5=3\\\\13-8=5\\\\21-13=8[/tex]
As the difference is not same.
Hence, option: C is not an arithmetic sequence.
D)
3,6,9,12,15
The difference is calculated as:
[tex]6-3=3\\\\9-6=3\\\\12-9=3\\\\15-12=3[/tex]
As the difference is same.
Hence, option: D is an arithmetic sequence.
