Problem

Find the $52^{\text {nd }}$ term of the following arithmetic sequence.
$14,23,32,41, \ldots$

Answer

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Answer

Final Answer: The $52^{ ext {nd }}$ term of the given arithmetic sequence is $oxed{473}$.

Steps

Step 1 :The given sequence is an arithmetic sequence. In an arithmetic sequence, the difference between any two successive members is a constant. This constant difference is also called the common difference. In this case, the common difference is $23 - 14 = 9$.

Step 2 :The formula to find the nth term of an arithmetic sequence is given by $a + (n - 1) * d$, where $a$ is the first term, $n$ is the term number, and $d$ is the common difference.

Step 3 :In this case, $a = 14$, $n = 52$, and $d = 9$.

Step 4 :So, we can substitute these values into the formula to find the 52nd term.

Step 5 :Calculating this gives us the 52nd term as 473.

Step 6 :Final Answer: The $52^{ ext {nd }}$ term of the given arithmetic sequence is $oxed{473}$.

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