Question

Let the sequence be 2, 8, 32, 128, ...... Then this sequence is:

A) Geometric and increasing.
B) Arithmetic and increasing.
C) Geometric and decreasing.
D) Arithmetic and decreasing.

Answer 1

The sequence 2, 8, 32, 128, ... is a geometric sequence that is increasing because each term is obtained by multiplying the previous term by a constant factor of 4.

Step-by-step explanation:

The given sequence is 2, 8, 32, 128, .... We can determine the nature of this sequence by examining the ratio of consecutive terms. The ratio between the second term (8) and the first term (2) is 8/2 = 4. Similarly, the ratio of the third term to the second term is 32/8 = 4, and the ratio of the fourth term to the third term is 128/32 = 4. Since each term is obtained by multiplying the previous term by a constant factor, which is 4 in this case, this sequence is a geometric sequence. Moreover, each term is larger than the preceding term, indicating that the sequence is increasing. Therefore, the correct answer is A) Geometric and increasing.