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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).

404,396,388,dots
Find the 44th 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). $\newline$ $404,396,388, \ldots$ $\newline$ Find the $44$ th term. $\newline$ Answer:

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Geometric sequences

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

404,396,388, \ldots

\newline

Find the

44

th term.

\newline

Answer:

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. $\newline$ The given sequence has a constant difference between consecutive terms. $\newline$ The given sequence is arithmetic.
Find Common Difference: Identify the common difference. $\newline$ Two consecutive terms are $404$ and $396$ . $\newline$ $396 - 404 = -8$ $\newline$ Common Difference: $-8$
Use Sequence Formula: Use the arithmetic sequence formula to find the $44^{\text{th}}$ term. $\newline$ The $n^{\text{th}}$ term of an arithmetic sequence is given by the formula: $\newline$ $a_n = a_1 + (n - 1)d$ $\newline$ where $a_n$ is the $n^{\text{th}}$ term, $a_1$ is the first term, $n$ is the term number, and $d$ is the common difference.
Calculate $44$ th Term: Calculate the $44$ th term using the formula. $\newline$ $a_{44} = 404 + (44 - 1)(-8)$ $\newline$ $a_{44} = 404 + 43(-8)$ $\newline$ $a_{44} = 404 - 344$ $\newline$ $a_{44} = 60$

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