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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).

11,15,19,dots
Find the 33rd 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). $\newline$ $11,15,19, \ldots$ $\newline$ Find the $33$ rd term. $\newline$ Answer:

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Powers with decimal bases

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

11,15,19, \ldots

\newline

Find the

33

rd term.

\newline

Answer:

Identify Pattern: Identify the pattern in the sequence. $\newline$ The sequence starts at $11$ and each term increases by $4$ ( $15 - 11 = 4$ , $19 - 15 = 4$ ). $\newline$ This is an arithmetic sequence with a common difference of $4$ .
Use Formula: Use the formula for the $n$ th term of an arithmetic sequence. $\newline$ The $n$ th term of an arithmetic sequence is given by $a_n = a_1 + (n - 1)d$ , where $a_1$ is the first term, $n$ is the term number, and $d$ is the common difference.
Plug in Values: Plug in the values for the $33^{\text{rd}}$ term. $a_1 = 11$ (the first term), $n = 33$ (since we want the $33^{\text{rd}}$ term), and $d = 4$ (the common difference). $a_{33} = 11 + (33 - 1) \times 4$
Perform Calculation: Perform the calculation. $\newline$ $a_{33} = 11 + (32 \times 4)$ $\newline$ $a_{33} = 11 + 128$ $\newline$ $a_{33} = 139$

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