QuestionListen
What expression do we get when we made a pattern by adding consecutive odd whole numbers? None of these possibilities are correct. $n+n$ $2 n$ $n^{2}$ $1+3+5+7+\ldots$

Studdy Solution

STEP 1

1. We are considering the sum of consecutive odd whole numbers.
2. We need to determine which expression correctly represents this sum.

STEP 2

1. Understand the pattern of adding consecutive odd numbers.
2. Derive a general formula for the sum of consecutive odd numbers.
3. Compare the derived formula with the given options.

STEP 3

Recognize the pattern of consecutive odd numbers: $1, 3, 5, 7, \ldots$ .

STEP 4

Notice that the sum of the first $n$ odd numbers is a known mathematical pattern.
The sum of the first $n$ odd numbers is given by the formula $n^2$ .

STEP 5

Compare the derived formula $n^2$ with the given options:
- $n+n$ simplifies to $2n$ , which is incorrect. - $2n$ is incorrect. - $n^2$ matches our derived formula. - The sequence $1+3+5+7+\ldots$ is represented by $n^2$ when summed up to the $n$ -th term.
The correct expression for the sum of consecutive odd numbers is:
$\boxed{n^2}$

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