Question

the first four terms of a sequence are shown on the graph.
(0, 1)
(1, 4)
(2, 16)
(3, 64)
a)
the sequence is ▼ because it has a common ▼ of ▼.
geometric
arithmetic
b) find the value o ▼

Explanation:

Step1: Identify Sequence Type

Check the ratio between consecutive terms. For \( n = 0 \) to \( n = 1 \): \( \frac{4}{1}=4 \). For \( n = 1 \) to \( n = 2 \): \( \frac{16}{4}=4 \). For \( n = 2 \) to \( n = 3 \): \( \frac{64}{16}=4 \). Since the ratio is constant, it's a geometric sequence.

Step2: Determine Common Ratio

The common ratio \( r \) is the constant ratio between terms, which we found as \( 4 \).

Answer:

a) The sequence is Geometric because it has a common ratio of \( 4 \).