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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).

403,395,387,dots
Find the 37th 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). $\newline$ $403,395,387, \ldots$ $\newline$ Find the $37$ th term. $\newline$ Answer:

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Find roots using a calculator

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

403,395,387, \ldots

\newline

Find the

37

th term.

\newline

Answer:

Determine Common Difference: First, we need to determine the common difference in the sequence by subtracting the second term from the first term and the third term from the second term. $\newline$ Calculation: $395 - 403 = -8$ and $387 - 395 = -8$ .
Confirm Arithmetic Sequence: Since the common difference is consistent, we can confirm that this is an arithmetic sequence with a common difference of $-8$ .
Find $37$ th Term Formula: To find the $37^{th}$ term, we 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.
Plug in Values: We plug in the values we know into the formula: $a_{37} = 403 + (37 - 1)(-8)$ .
Calculate Term: Now we calculate the term inside the parentheses: $37 - 1 = 36$ .
Multiply Common Difference: Next, we multiply $36$ by the common difference $-8$ : $36 \times -8 = -288$ .
Add to Find $37$ th Term: Finally, we add this result to the first term to find the $37$ th term: $403 + (-288) = 115$ .

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