Question

For the following​ sequence, determine if it is an arithmetic​sequence, a geometric​ sequence, or neither. If it is either arithmetic or​ geometric, give the next term in the sequence.
5​, 8​,13​, 21​, 34​, 55,...

Answer 1

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.

$a_1=5,a_2=8,a_3=13,...a_6=55$

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.

$d_1=a_2-a_1=8-5=3$

$d_2=a_3-a_2=13-8=5$

$d_1\neq d_2$

Hence, the difference between the consecutive terms is not equal .Therefore, sequence is not an arithmetic sequence.

$r_1=\frac{a_2}{a_1}=\frac{8}{5}$

$r_2=\frac{a_3}{a_2}=\frac{13}{8}$

$r_1\neq r_2$

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.