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

10,14,18, \ldots

\newline

Find the

47

th term.

\newline

Answer:

Identify Pattern: Identify the pattern in the sequence. $\newline$ The sequence starts at $10$ and each term increases by $4$ ( $14 - 10 = 4$ , $18 - 14 = 4$ ). $\newline$ 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 ( $a_n$ ) 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 in Values: Plug in the values for the $47^{\text{th}}$ term. $a_1 = 10$ (the first term) $n = 47$ (we want to find the $47^{\text{th}}$ term) $d = 4$ (the common difference)Now, calculate the $47^{\text{th}}$ term using the formula: $a_{47} = 10 + (47 - 1) \times 4$
Perform Calculation: Perform the calculation. $\newline$ $a_{47} = 10 + (46 \times 4)$ $\newline$ $a_{47} = 10 + 184$ $\newline$ $a_{47} = 194$