Answer:
Neither
Step-by-step explanation:
We are given that a sequence
5,8,13,21,34,55,....
We have to determine the sequence is an arithmetic , geometric or neither.
[tex]a_1=5,a_2=8,a_3=13,...a_6=55[/tex]
We know that if a sequence is an arithmetic then the difference between consecutive terms are equal.
If a sequence is geometric then the ratio of consecutive terms is constant.
[tex]d_1=a_2-a_1=8-5=3[/tex]
[tex]d_2=a_3-a_2=13-8=5[/tex]
[tex]d_1\neq d_2[/tex]
Hence, the difference between the consecutive terms is not equal .Therefore, sequence is not an arithmetic sequence.
[tex]r_1=\frac{a_2}{a_1}=\frac{8}{5}[/tex]
[tex]r_2=\frac{a_3}{a_2}=\frac{13}{8}[/tex]
[tex]r_1\neq r_2[/tex]
Hence, the ratio of consecutive terms is not equal .Therefore, given sequence is not geometric sequence.
Therefore, given sequence is not an arithmetic nor geometric sequence.
