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Mathematics > Standard Multiple Choice

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The first four terms of a sequence are shown above. Which of the following could be the formula that gives the th term of this sequence for all positive integers ?

# Correct!

### Explanation

If a formula gives the th term of the sequence for all positive integers , it must give the th term of the sequence for . If , then and , but the first term of the sequence is , so the general formula cannot be or . Also, if , then and , but the third term of the sequence is , so the general formula cannot be or . However, for , the values of are , , , , respectively. Therefore, the general formula for this sequence could be .

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