Write an explicit formula for a_(n), the n^("th ") term of the sequence 80,20,5,dots Answer: a_(n)=

Identify Pattern: Identify the pattern in the sequence. The given sequence is 80, 20, 5, ... Each term is divided by 4 to get the next term. This indicates that the sequence is a geometric sequence.Determine Common Ratio: Determine the common ratio (r) of the sequence. To find the common ratio, divide the second term by the first term. r = 20 / 80 = 1/4Write Formula: Write the formula for the nth term of a geometric sequence. The nth term of a geometric sequence is given by a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.Substitute Values: Substitute the known values into the formula. The first term a_1 is 80 and the common ratio r is 1/4. a_n = 80 * (1/4)^(n-1)

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Write an explicit formula for
a_(n), the
n^("th ") term of the sequence
80,20,5,dots
Answer:
a_(n)=

Write an explicit formula for $a_{n}$ , the $n^{\text {th }}$ term of the sequence $80,20,5, \ldots$ $\newline$ Answer: $a_{n}=$ $\newline$

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Math Problems

Algebra 1

Write variable expressions for arithmetic sequences

Full solution

Q. Write an explicit formula for

a_{n}

, the

n^{\text {th }}

term of the sequence

80,20,5, \ldots

\newline

Answer:

a_{n}=

\newline

Identify Pattern: Identify the pattern in the sequence. $\newline$ The given sequence is $80, 20, 5, \ldots$ Each term is divided by $4$ to get the next term. This indicates that the sequence is a geometric sequence.
Determine Common Ratio: Determine the common ratio $r$ of the sequence. $\newline$ To find the common ratio, divide the second term by the first term. $\newline$ $r = \frac{20}{80} = \frac{1}{4}$
Write Formula: Write 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 and $r$ is the common ratio.
Substitute Values: Substitute the known values into the formula. $\newline$ The first term $a_1$ is $80$ and the common ratio $r$ is $\frac{1}{4}$ . $\newline$ $a_n = 80 \times \left(\frac{1}{4}\right)^{n-1}$