Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If
a_(1)=3 and
a_(n+1)=(a_(n))^(2)-1 then find the value of
a_(3).
Answer:

If $a_{1}=3$ and $a_{n+1}=\left(a_{n}\right)^{2}-1$ then find the value of $a_{3}$ . $\newline$ Answer:

View step-by-step help

View step-by-step help

Transformations of functions

Full solution

Q. If

a_{1}=3

and

a_{n+1}=\left(a_{n}\right)^{2}-1

then find the value of

a_{3}

.

\newline

Answer:

Given terms and formula: We are given the first term of the sequence, $a_{1} = 3$ , and the recursive formula for the sequence, $a_{n+1} = (a_{n})^2 - 1$ . To find $a_{3}$ , we first need to find $a_{2}$ using the given formula.
Find $a_{2}$ : Using the recursive formula $a_{n+1} = (a_{n})^2 - 1$ , we substitute $n = 1$ to find $a_{2}$ :
$a_{2} = (a_{1})^2 - 1$
$a_{2} = (3)^2 - 1$
$a_{2} = 9 - 1$
$a_{2} = 8$
Find $a_{3}$ : Now that we have $a_{2}$ , we can use it to find $a_{3}$ using the same recursive formula: $\newline$ $a_{3} = (a_{2})^2 - 1$ $\newline$ $a_{3} = (8)^2 - 1$ $\newline$ $a_{3} = 64 - 1$ $\newline$ $a_{3} = 63$

More problems from Transformations of functions

Question

g(x)

g(x)

is the reflection across the x-axis of

f(x)=9|x+2|-4

\newline

\newline

\text{}(A)g(x) = 9|x+2| - 4\text{]}

\newline

\text{}(B)g(x) = 9|x-2| - 4\text{]}

\newline

\text{}(C)g(x)=-9|x-2| +4\text{]}

\newline

\text{(D)}g(x) = -9|x + 2| + 4\text{]}

Posted 3 months ago

Question

What does the transformation

f(x) \mapsto f(x - 4)

do to the graph of

f(x)

\newline

\newline

\text{translates it } 4 \text{ units right}

\newline

\text{translates it } 4 \text{ units down}

\newline

\text{translates it } 4 \text{ units left}

\newline

\text{translates it } 4 \text{ units up}

Posted 3 months ago

Question

What does the transformation

f(x) \mapsto f(4x)

do to the graph of

f(x)

\newline

\newline

[A] stretches it vertically

\newline

[B] stretches it horizontally

\newline

[C]shrinks it horizontally

\newline

[D]shrinks it vertically

Posted 2 months ago

Question

g(x)

g(x)

is the translation

9

f(x) = 10x + 8

\newline

\newline

g(x) = 10x - 82

\newline

g(x) = 10x + 98

\newline

g(x) = 10x - 1

\newline

g(x) = 10x + 17

Posted 3 months ago

Question

What kind of transformation converts the graph of

f(x) = -3x^2 - 4

into the graph of

g(x) = -3x^2 + 6

\newline

\newline

\text{[A]translation 10 units up}

\newline

\text{[B]translation 10 units down}

\newline

\text{[C]translation 10 units left}

\newline

\text{[D]translation 10 units right}

Posted 2 months ago

Question

y=x^{2}

is scaled vertically by a factor of

7

. What is the equation of the new parabola?

\newline

y=

Posted 4 months ago

Question

y=x^{2}

is shifted down by

6

units and to the right by

5

\newline

What is the equation of the new parabola?

\newline

y=

Posted 4 months ago

Question

y=x^{2}

is shifted up by

2

units and to the right by

3

\newline

What is the equation of the new parabola?

\newline

y=

Posted 2 months ago

Question

y=x^{2}

is reflected across the

x

-axis and then scaled vertically by a factor of

5

\newline

What is the equation of the new parabola?

\newline

y=\square

Posted 2 months ago

Question

y=x^{2}

is scaled vertically by a factor of

\frac{1}{10}

\newline

What is the equation of the new parabola?

\newline

y=

Posted 3 months ago