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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).

461,452,443,dots
Find the 39th 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). $\newline$ $461,452,443, \ldots$ $\newline$ Find the $39$ th 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

461,452,443, \ldots

\newline

Find the

39

th term.

\newline

Answer:

Identify Pattern: The question prompt is: ＂What is the $39$ th term of the sequence $461, 452, 443, \ldots$ ?＂
Find Common Difference: Identify the pattern in the sequence. The sequence decreases by $9$ each time ( $461 - 452 = 9$ , $452 - 443 = 9$ ).
Use Formula for nth Term: Determine the common difference of the arithmetic sequence. The common difference $d$ is $-9$ .
Substitute Values: Use the formula for the $n$ th term of an arithmetic sequence: $a_n = a_1 + (n - 1)d$ , 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.
Calculate Inside Parentheses: Substitute the known values into the formula to find the $39^{th}$ term. Here, $a_1 = 461$ , $n = 39$ , and $d = -9$ . $\newline$ $a_{39} = 461 + (39 - 1)(-9)$
Multiply Common Difference: Calculate the value inside the parentheses first: $(39 - 1) = 38$ .
Add to First Term: Multiply the common difference by $38$ : $38 \times (-9) = -342$ .
Final Answer: Add the result to the first term: $461 + (-342) = 119$ .
Final Answer: Add the result to the first term: $461 + (-342) = 119$ . The $39$ th term of the sequence is $119$ . There is no need to round since it is a whole number.

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