Question

fiona wrote the sequence below:
3, 12, 48, 192, ...
(arrows with ×4 between each term)
which of the following classifies the sequence?

• arithmetic
• geometric
• both arithmetic and geometric
• neither arithmetic nor geometric

Explanation:

Step1: Recall sequence types

An arithmetic sequence has a common difference (subtracting consecutive terms gives the same value). A geometric sequence has a common ratio (dividing consecutive terms gives the same value).

Step2: Check arithmetic (common difference)

Calculate differences: \(12 - 3 = 9\), \(48 - 12 = 36\), \(192 - 48 = 144\). Differences are not equal, so not arithmetic.

Step3: Check geometric (common ratio)

Calculate ratios: \(\frac{12}{3} = 4\), \(\frac{48}{12} = 4\), \(\frac{192}{48} = 4\). Common ratio exists, so geometric.

Answer:

geometric