Arithmetic vs. Geometric: Identification and Comparison

Practice & Review

Test your ability to distinguish between arithmetic and geometric sequences. This stack provides mixed sequences and asks you to identify the pattern—common difference or common ratio—and classify them accordingly.

Arithmetic vs. Geometric: Identification and Comparison

1 of 11

What is the key difference between how terms are generated in an arithmetic versus a geometric sequence?

In an arithmetic sequence, you add a constant difference. In a geometric sequence, you multiply by a constant ratio.

To determine if a sequence is arithmetic, what should you do?

Subtract consecutive terms (\(a_{n+1} - a_n\)) and check if the difference is constant.

To determine if a sequence is geometric, what should you do?

Divide consecutive terms (\(\frac{a_{n+1}}{a_n}\)) and check if the ratio is constant.

Identify the sequence type: \(2, 6, 18, 54, ...\)

Geometric. Each term is multiplied by \(3\). The common ratio is \(r = 3\).

Identify the sequence type: \(2, 6, 10, 14, ...\)

Arithmetic. A constant value of \(4\) is added to each term. The common difference is \(d = 4\).

Identify the sequence type: \(-1, -5, -9, -13, ...\)

Arithmetic. A constant value of \(-4\) is added to each term. The common difference is \(d = -4\).

Identify the sequence type: \(48, 24, 12, 6, ...\)

Geometric. Each term is multiplied by \(\frac{1}{2}\). The common ratio is \(r = 0.5\).

Identify the sequence type: \(1, 1, 2, 3, 5, 8, ...\) (The Fibonacci Sequence)

Neither. There is no common difference or common ratio between consecutive terms.

Identify the sequence type: \(5, 8, 12, 17, 23, ...\)

Neither. The differences are \(3\), \(4\), \(5\), \(6\), and the ratios are not constant. The pattern is not arithmetic or geometric.

A sequence's explicit formula is \(a_n = 5n - 2\). Is it arithmetic or geometric?

Arithmetic. The formula is linear, with a common difference (slope) of \(d=5\).

A sequence's explicit formula is \(a_n = 3 \cdot (\frac{1}{2})^{n-1}\). Is it arithmetic or geometric?

Geometric. The formula is exponential, with a common ratio of \(r = \frac{1}{2}\).

Arithmetic vs. Geometric: Identification and Comparison

Confirm Action

Prompt