Problem

Find the $72^{\text {nd }}$ term of the following arithmetic sequence.
\[
16,19,22,25, \ldots
\]

Answer

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Answer

Final Answer: The $72^{\text {nd }}$ term of the arithmetic sequence is \(\boxed{229}\)

Steps

Step 1 :This is an arithmetic sequence, which means each term is obtained by adding a constant difference to the previous term. In this case, the common difference is 3 (19-16 = 3).

Step 2 :The formula to find the nth term of an arithmetic sequence is given by: \(a_n = a_1 + (n-1)*d\) where \(a_n\) is the nth term, \(a_1\) is the first term, \(d\) is the common difference, and \(n\) is the position of the term in the sequence.

Step 3 :In this case, \(a_1 = 16\), \(d = 3\), and \(n = 72\). We can substitute these values into the formula to find the 72nd term.

Step 4 :Using the formula, we get \(a_n = 16 + (72-1)*3 = 229\)

Step 5 :Final Answer: The $72^{\text {nd }}$ term of the arithmetic sequence is \(\boxed{229}\)

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