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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).

2,10,50,dots
Find the 8th 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). $\newline$ $2,10,50, \ldots$ $\newline$ Find the $8$ 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

2,10,50, \ldots

\newline

Find the

8

th term.

\newline

Answer:

Identify Pattern: Identify the pattern in the sequence. $\newline$ The sequence starts with $2$ , and each term is multiplied by $5$ to get the next term ( $2 \times 5 = 10$ , $10 \times 5 = 50$ ). $\newline$ This is a geometric sequence with a common ratio of $5$ .
Use Formula: Use the formula for the $n$ th term of a geometric sequence. $\newline$ The $n$ th term ( $a_n$ ) of a geometric sequence can be found using the formula $a_n = a_1 \cdot r^{(n-1)}$ , where $a_1$ is the first term and $r$ is the common ratio.
Plug in Values: Plug in the values for the $8$ th term. $\newline$ $a_1 = 2$ (the first term), $r = 5$ (the common ratio), and $n = 8$ (the term number we want to find). $\newline$ $a_8 = 2 \times 5^{8-1} = 2 \times 5^7$
Calculate $8$ th Term: Calculate the $8$ th term. $a_8 = 2 \times 5^7 = 2 \times 78125 = 156250$

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