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The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary).

452,443,434,dots
Find the 32nd term.
Answer:

The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary). $\newline$ $452,443,434, \ldots$ $\newline$ Find the $32$ nd term. $\newline$ Answer:

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Find probabilities using combinations and permutations

Full solution

Q. The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary).

\newline

452,443,434, \ldots

\newline

Find the

32

nd term.

\newline

Answer:

Identify Pattern: First, let's identify the pattern in the sequence. We notice that each term is $9$ less than the previous term.
Find Common Difference: To find the $32$ nd term, we need to determine the common difference and use the formula for the $n$ th term of an arithmetic sequence, which is $a_n = a_1 + (n - 1)d$ , where $a_n$ is the $n$ th term, $a_1$ is the first term, $n$ is the term number, and $d$ is the common difference.
Substitute Values: The common difference $d$ is the difference between any two consecutive terms, which we have identified as $-9$ .
Calculate Term Number: Now we substitute the known values into the formula: $a_{32} = 452 + (32 - 1)(-9)$ .
Perform Multiplication: Calculate the term number and the common difference: $a_{32} = 452 + 31(-9)$ .
Subtract to Find Term: Perform the multiplication: $a_{32} = 452 - 279$ .
Final Result: Now, subtract to find the $32^{\text{nd}}$ term: $a_{32} = 173$ .
Final Result: Now, subtract to find the $32^{\text{nd}}$ term: $a_{32} = 173$ .We have found the $32^{\text{nd}}$ term of the sequence, which is $173$ . There is no need to round since it is a whole number.

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