Question

50, 40, 32, 128/5 ...
A. Geometric
B. Arithmetic
C. Both

Answer 1

The correct answer is A.

50(4/5) = 40, 40(4/5) = 32, 32(4/5) = 128/5

This is a geometric sequence.

Answer 2

The given sequence is geometric, and the correct answer is option A.

Step-by-step explanation:

The given sequence is 50, 40, 32, 128/5.

To determine whether the sequence is arithmetic, geometric, or both, we first need to find the common difference or common ratio.

In an arithmetic sequence, the common difference between consecutive terms is constant. In a geometric sequence, the common ratio between consecutive terms is constant.

Let's analyze the given sequence:

50, 40, 32, 128/5

Observing the differences between consecutive terms, we have:

40 - 50 = -10

32 - 40 = -8

128/5 - 32 = 128/5 - 160/5 = -32/5

The differences between consecutive terms are not constant, which means the sequence is not arithmetic.

Now let's analyze the ratios between consecutive terms:

40/50 = 4/5

32/40 = 4/5

128/5 ÷ 32 = (128/5) × (5/32) = 128/32 = 4

The ratios between consecutive terms are constant (4/5), which means the sequence is geometric.

Therefore, the sequence is geometric, and the correct answer is option A.