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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).

4,11,18,dots
Find the 42nd 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). $\newline$ $4,11,18, \ldots$ $\newline$ Find the $42$ nd 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

4,11,18, \ldots

\newline

Find the

42

nd term.

\newline

Answer:

Identify pattern: Identify the pattern in the sequence. $\newline$ The sequence starts with $4$ and each term increases by $7$ ( $11 - 4 = 7$ , $18 - 11 = 7$ ). $\newline$ This is an arithmetic sequence with a common difference of $7$ .
Use formula: Use the formula for the $n$ th term of an arithmetic sequence. $\newline$ The $n$ th term ( $a_n$ ) of an arithmetic sequence can be found using the formula: $\newline$ $a_n = a_1 + (n - 1)d$ $\newline$ where $a_1$ is the first term, $n$ is the term number, and $d$ is the common difference.
Plug values: Plug in the values for the $42^{\text{nd}}$ term. $a_1 = 4$ (the first term) $n = 42$ (the term number we want to find) $d = 7$ (the common difference) $a_{42} = 4 + (42 - 1) \times 7$
Perform calculation: Perform the calculation. $\newline$ $a_{42} = 4 + (41) \times 7$ $\newline$ $a_{42} = 4 + 287$ $\newline$ $a_{42} = 291$

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