Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$f(n)=-48*(-(1)/(4))^(n) Complete the recursive formula of f(n). {:[f(1)=◻],[f(n)=f(n-1)]:}$

$f(n)=-48 \cdot\left(-\frac{1}{4}\right)^{n}$ $\newline$ Complete the recursive formula of $f(n)$ . $\newline$ $\begin{array}{l} f(1)=\square \\ f(n)=f(n-1) \cdot \square \end{array}$

View step-by-step help

View step-by-step help

Write variable expressions for geometric sequences

Full solution

Q.

f(n)=-48 \cdot\left(-\frac{1}{4}\right)^{n}

\newline

Complete the recursive formula of

f(n)

.

\newline

\begin{array}{l} f(1)=\square \\ f(n)=f(n-1) \cdot \square \end{array}

Given explicit formula: We are given the explicit formula for the sequence: $\newline$ $f(n) = -48 \cdot \left(-\left(\frac{1}{4}\right)\right)^n$ $\newline$ To find the recursive formula, we need to express $f(n)$ in terms of $f(n-1)$ . $\newline$ First, let's find $f(1)$ by substituting $n = 1$ into the explicit formula. $\newline$ $f(1) = -48 \cdot \left(-\left(\frac{1}{4}\right)\right)^1$ $\newline$ $f(1) = -48 \cdot \left(-\frac{1}{4}\right)$ $\newline$ $f(1) = \frac{48}{4}$ $\newline$ $f(1) = 12$
Find $f(1)$ : Now, let's find $f(2)$ to see the relationship between $f(2)$ and $f(1)$ .
$f(2) = -48 \times (-(1/4))^2$
$f(2) = -48 \times (1/16)$
$f(2) = -48/16$
$f(2) = -3$
Find $f(2)$ : We can see that to go from $f(1)$ to $f(2)$ , we multiply $f(1)$ by $-\left(\frac{1}{4}\right)$ :
$f(2) = f(1) \times -\left(\frac{1}{4}\right)$
$f(2) = 12 \times -\left(\frac{1}{4}\right)$
$f(2) = -3$
This relationship holds for each subsequent term in the sequence.
Relationship between $f(1)$ and $f(2)$ : Therefore, the recursive formula for the sequence is: $\newline$ $f(1) = 12$ $\newline$ $f(n) = f(n-1) \times -(\frac{1}{4})$ for $n > 1$

More problems from Write variable expressions for geometric sequences

Question

What is the period of

\newline

y=-2 \sin \left(\frac{2}{3} x-4\right) ?

\newline

Give an exact value.

\newline

Posted 3 months ago

Question

What is the period of

\newline

y=8 \cos \left(5 \pi x+\frac{3 \pi}{2}\right)-9 ?

\newline

Give an exact value.

\newline

Posted 3 months ago

Question

z=91-27 i

\newline

What is the real part of

z

\newline

What is the imaginary part of

z

Posted 3 months ago

Question

z=-19 i+14

\newline

What is the real part of

z

\newline

What is the imaginary part of

z

Posted 3 months ago

Question

z=-302+19.3 i

\newline

What is the real part of

z

\newline

What is the imaginary part of

z

Posted 3 months ago

Question

The sum of the first

3

terms of a geometric series is

171

and the common ratio is

\frac{2}{3}

\newline

What is the first term of the series?

Posted 3 months ago

Question

The first term in a geometric series is

5

and the common ratio is

2

\newline

Find the sum of the first

10

terms in the series.

Posted 3 months ago

Question

What happens to the value of the expression

70-3 g

g

\newline

1

\newline

(A) It increases.

\newline

(B) It decreases.

\newline

(C) It stays the same.

Posted 3 months ago

Question

What happens to the value of the expression

m-10

m

\newline

1

\newline

(A) It increases.

\newline

(B) It decreases.

\newline

(C) It stays the same.

Posted 3 months ago

Question

What happens to the value of the expression

20+a

a

\newline

1

\newline

(A) It increases.

\newline

(B) It decreases.

\newline

(C) It stays the same.

Posted 3 months ago