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

Identify Sequence Pattern: To find the explicit formula for the nth term of the sequence, we first need to determine the pattern of the sequence. Looking at the sequence 150, 30, 6, ..., we can see that each term is divided by 5 to get the next term. This indicates that the sequence is a geometric sequence with a common ratio of 1/5.General Form of nth Term: The general form of 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. For our sequence, a_1 = 150 and r = 1/5.Substitute Values and Simplify: Now we can substitute the values of a_1 and r into the formula to get the explicit formula for the nth term: a_n = 150 * (1/5)^(n-1) This is the explicit formula for the nth term of the given sequence.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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: $a_{n}=$

View step-by-step help

Home

Math Problems

Algebra 2

Transformations of quadratic functions

Full solution

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 Sequence Pattern: To find the explicit formula for the $n$ th term of the sequence, we first need to determine the pattern of the sequence. $\newline$ Looking at the sequence $150, 30, 6, \ldots$ , we can see that each term is divided by $5$ to get the next term. $\newline$ This indicates that the sequence is a geometric sequence with a common ratio of $\frac{1}{5}$ .
General Form of nth Term: The general form of the nth term of a geometric sequence is given by: $\newline$ $a_n = a_1 \times r^{(n-1)}$ $\newline$ where $a_1$ is the first term and $r$ is the common ratio. $\newline$ For our sequence, $a_1 = 150$ and $r = \frac{1}{5}$ .
Substitute Values and Simplify: Now we can substitute the values of $a_1$ and $r$ into the formula to get the explicit formula for the $n$ th term: $\newline$ $a_n = 150 \times (\frac{1}{5})^{(n-1)}$ $\newline$ This is the explicit formula for the $n$ th term of the given sequence.