Write an explicit formula for a_(n), the n^("th ") term of the sequence 150,30,6,dots. Answer: a_(n)=

Identify Pattern: Identify the pattern in the sequence. The sequence is 150, 30, 6, ... Each term is divided by 5 to get the next term. This is a geometric sequence with a common ratio of 1/5.Determine First Term: Determine the first term (a_1) of the sequence. The first term of the sequence is 150.Find Common Ratio: Determine the common ratio (r) of the sequence. The common ratio is the factor by which we multiply each term to get the next term. In this case, r = 1/5.Write Explicit Formula: Write the explicit formula for the nth term of a geometric sequence. The explicit formula for the nth term of a geometric sequence is a_n = a_1 * r^(n-1).Substitute Values: Substitute the values of a_1 and r into the formula. a_n = 150 * (1/5)^(n-1).

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Write an explicit formula for
a_(n), the
n^("th ") term of the sequence
150,30,6,dots.
Answer:
a_(n)=

Write an explicit formula for $a_{n}$ , the $n^{\text {th }}$ term of the sequence $150,30,6, \ldots$ . $\newline$ Answer: $a_{n}=$

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Math Problems

Algebra 2

Evaluate exponential functions

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Q. Write an explicit formula for

a_{n}

, the

n^{\text {th }}

term of the sequence

150,30,6, \ldots

\newline

Answer:

a_{n}=

Identify Pattern: Identify the pattern in the sequence. $\newline$ The sequence is $150, 30, 6, \ldots$ Each term is divided by $5$ to get the next term. This is a geometric sequence with a common ratio of $\frac{1}{5}.$
Determine First Term: Determine the first term $a_1$ of the sequence. $\newline$ The first term of the sequence is $150$ .
Find Common Ratio: Determine the common ratio $r$ of the sequence. $\newline$ The common ratio is the factor by which we multiply each term to get the next term. In this case, $r = \frac{1}{5}$ .
Write Explicit Formula: Write the explicit formula for the $n$ th term of a geometric sequence. $\newline$ The explicit formula for the $n$ th term of a geometric sequence is $a_n = a_1 \cdot r^{(n-1)}$ .
Substitute Values: Substitute the values of $a_1$ and $r$ into the formula. $\newline$ $a_n = 150 \times (\frac{1}{5})^{(n-1)}$ .