Problem

Row \(1\) has \(10~\text{seats}\), and each later row has \(2~\text{more}~\text{seats}\). A student proposes \(a_{n}~=~10~+~2n\) for \(n~=~1,~2,~3,~\ldots~\). Compare the required and proposed starting values, diagnose the indexing error, and write the corrected rule.

Big Picture

What this problem is really about

The fastest way to diagnose a sequence-indexing error is to test the stated first index. We’ll compare the proposed first output with the required starting value, verify the common difference separately, and count how many transitions actually occur before term n. Correcting only that transition count preserves the rate while restoring the proper start and discrete domain.

Answer choices

Choose your path.

Preview only

The required start is a₁ = 10 and the proposal gives a₁ = 12, but there is no error; aₙ = 10 + 2n for n ≥ 1.

The required start is a₁ = 10, but the proposal gives a₁ = 12. The common difference is wrong; aₙ = 10 + n for n ≥ 1.

The required start is a₁ = 10, but the proposal gives a₁ = 12. The increase was applied one row too early; aₙ = 10 + 2(n - 1) for n = 1, 2, 3, …

The required start is a₀ = 10 and the proposal gives a₀ = 10, so there is no error; aₙ = 10 + 2n for n ≥ 0.

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Row \(1\) has \(10~\text{seats}\), and each later row has \(2~\text{more}~\text{seats}\). A student proposes \(a_{n}~=~10~+~2n\) for \(n~=~1,~2,~3,~\ldots~\). Compare the required and proposed starting values, diagnose the indexing error, and write the corrected rule.

What this problem is really about

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.