In the sequence 21,700, 23,172, 24,644, 26,116,... which term is 314,628?

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Identify the type of sequence given. Since the difference between consecutive terms is constant, this is an arithmetic sequence.

Calculate the common difference $d$ by subtracting the first term from the second term: $d = 23,172 - 21,700$.

Use the formula for the $n$-th term of an arithmetic sequence: $a_n = a_1 + (n - 1) \times d$, where $a_1$ is the first term and $d$ is the common difference.

Set $a_n$ equal to 314,628 and substitute $a_1$ and $d$ into the formula: $314,628 = 21,700 + (n - 1) \times d$.

Solve the equation for $n$ to find which term in the sequence is 314,628.

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Arithmetic Sequence

An arithmetic sequence is a list of numbers where each term after the first is found by adding a constant difference to the previous term. Recognizing this pattern helps in identifying the common difference and formulating the general term.

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The nth term of an arithmetic sequence can be expressed as a_n = a_1 + (n - 1)d, where a_1 is the first term and d is the common difference. This formula allows us to find any term in the sequence given its position.

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