The table below gives the positions of three terms in an arithmetic sequence What is the n^ (th ) term rule for the sequence? Position, n & ldots & 100 & 101 & 102 Term & ldots & 324 & 327 & 330

## Step 1: Identify the common difference of the arithmetic sequenceBy looking at the given numbers in the sequence, namely , , and , we can see that the common difference, , is .## Step 2: Identify the first term of the sequenceSince the common difference is known, the first term of the sequence can be found by subtracting [(position - 1) common difference] from any known term. Let's take the term, subtracting (This consists of 99 steps of +3 from the first term)### \(a _ { 1 } = a - (n-1) \cdot d\)### \(a_{1} = 324 - (100-1) \cdot 3\)### ## Step 3: Write out the nth term rule for the sequenceThe "nth term" or general rule of an arithmetic sequence is \(a_n = a_1 + (n-1)d\), where is the nth term, is the first term, is the common difference and is the term number. Substituting the values that we computed before for and , the formula becomes### \(a_n = 27 + 3(n-1)\)This formula allows you to find any term in the sequence knowing its position.