Question

Is this sequence arithmetic, geometric, or neither?

Answer 1

It is a geometric sequence

Answer 2

Answer:

Geometric

Step-by-step explanation:

An arithmetic sequence has to have a constan increse or decrease. as we can see between 96 and 72 we have a decreases of 24 units, between 72 and 54 the distance is of 18 unit and finally betweent 54 and 40.5 the distance is 13.5 units. Due to the distance between two consecutive the terms of the sequence is not always the same it is not a arithmetic sequence.

Now in the case of geometric sequence to find the terms of the sequence we need to multiply one term by a number to find the next term. Then if the sequence is geometric we just need to take one term and divide it by the previous one to find the number that generate te sequence, then:

$\dfrac{72}{96}=0.75$

To check if this is a geometric sequence, we need to multiply each term by 0.75 and the result have to be the next term, then:

$96\cdot 0.75=72\\72\cdot 0.75=54\\54\cdot 0.75=40.5$

With this result we can conclude that the sequence is Geometric.