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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).

14,28,56,dots
Find the 6th 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). $\newline$ $14,28,56, \ldots$ $\newline$ Find the $6$ th 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

14,28,56, \ldots

\newline

Find the

6

th term.

\newline

Answer:

Identify Pattern: Identify the pattern in the sequence. $\newline$ The given sequence is $14$ , $28$ , $56$ . We notice that each term is double the previous term. $\newline$ $14 \times 2 = 28$ $\newline$ $28 \times 2 = 56$ $\newline$ This is a geometric sequence with a common ratio of $2$ .
Use Formula: Use the formula for the $n$ th term of a geometric sequence. $\newline$ The $n$ th term of a geometric sequence is given by $a_n = a_1 \cdot r^{(n-1)}$ , where $a_1$ is the first term, $r$ is the common ratio, and $n$ is the term number. $\newline$ For this sequence, $a_1 = 14$ and $r = 2$ .
Calculate $6$ th Term: Calculate the $6$ th term using the formula. $\newline$ $a_6 = 14 \times 2^{6-1}$ $\newline$ $a_6 = 14 \times 2^5$ $\newline$ $a_6 = 14 \times 32$ $\newline$ $a_6 = 448$

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