Question

Is the sequence arithmetic, geometric, or neither?

Un = 3(2.5)^(n-1)
A) Arithmetic
B) Geometric
C) both
D) none of the above

Answer 1

The sequence is geometric because each term is multiplied by a constant ratio of 2.5 to obtain the next term; it is not arithmetic as it does not involve adding a constant difference.

Step-by-step explanation:

The sequence Un = 3(2.5)(n-1) is a geometric sequence. This type of sequence is identified by each term being multiplied by a constant amount, known as the common ratio, to get the next term. In this case, the common ratio is 2.5, since every term is multiplied by 2.5 to obtain the next term. This does not fit the definition of an arithmetic sequence, which would require that each term is obtained by adding a constant difference. Thus, the sequence is geometric and not arithmetic.