Resources

Resources

Bytelearn - cat image with glasses

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
37,31,25,dots.
Answer:
a_(n)=

Write an explicit formula for $a_{n}$ , the $n^{\text {th }}$ term of the sequence $37,31,25, \ldots$ . $\newline$ Answer: $a_{n}=$

View step-by-step help

View step-by-step help

Transformations of quadratic functions

Full solution

Q. Write an explicit formula for

a_{n}

, the

n^{\text {th }}

term of the sequence

37,31,25, \ldots

.

\newline

Answer:

a_{n}=

Calculate Common Difference: To find the explicit formula for the $n$ th term of the sequence, we first need to determine the common difference between the terms. We do this by subtracting any term from the term that follows it. $\newline$ Calculation: $31 - 37 = -6$
Arithmetic Sequence Formula: The common difference is $-6$ , which means the sequence is arithmetic and each term is $6$ less than the term before it. The explicit formula for an arithmetic sequence is given by: $\newline$ $a_n = a_1 + (n - 1)d$ $\newline$ where $a_1$ is the first term and $d$ is the common difference.
Substitute Values: We know the first term $a_1$ is $37$ and the common difference $d$ is $-6$ . Now we can substitute these values into the formula to find the explicit formula for $a_n$ . $\newline$ Calculation: $a_n = 37 + (n - 1)(-6)$
Distribute $-6$ : Simplify the formula by distributing the $-6$ into the parentheses. $\newline$ Calculation: $a_n = 37 - 6(n - 1)$
Multiply Terms: Further simplify the formula by multiplying out the terms inside the parentheses. $\newline$ Calculation: $a_n = 37 - 6n + 6$
Combine Like Terms: Combine like terms to get the final explicit formula for the nth term of the sequence. $\newline$ Calculation: $a_n = 43 - 6n$

More problems from Transformations of quadratic functions

Question

Solve by completing the square.

\newline

m^2 - 10m - 29 = 0

\newline

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

\newline

`m` = ____ or `m` = _____

Posted 2 months ago

Question

g(x)

g(x)

is the translation

5

f(x)=x^2

\newline

Write your answer in the form

a(x–h)^2+k

a

h

k

\newline

g(x)=

Posted 2 months ago

Question

What is the range of this quadratic function?

\newline

y = x^2 - 4x + 4

\newline

\newline

\left\{y \mid y \geq 2\right\}

\newline

\left\{y \mid y \leq 0\right\}

\newline

\left\{y \mid y \geq 0\right\}

\newline

\text{all real numbers}

Posted 2 months ago

Question

Write the equation of the parabola that passes through the points

(1,0)

(2,0)

(3,\text{–}16)

. Write your answer in the form

y = a(x – p)(x – q)

a

p

q

are integers, decimals, or simplified fractions.

\newline

Posted 2 months ago

Question

Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

\newline

f^2 + 8f + \_\_\_\_\_

Posted 2 months ago

Question

h

\newline

h^2 + 39h = 0

\newline

\newline

Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

\newline

h =

\newline

Posted 2 months ago

Question

Write a quadratic function with zeros

-9

-7

\newline

Write your answer using the variable

x

and in standard form with a leading coefficient of

1

\newline

f(x) = \_\_\_\_\_

Posted 2 months ago

Question

Find the equation of the axis of symmetry for the parabola

y = x^2

\newline

Simplify any numbers and write them as proper fractions, improper fractions, or integers.

\newline

\underline{\hspace{3cm}}

Posted 3 months ago

Question

g(x)

g(x)

is the translation

8

f(x) = x^2

\newline

Write your answer in the form

a(x – h)^2 + k

a

h

k

\newline

g(x) =

\newline

Posted 3 months ago

Question

x

\newline

x^2 = 1

\newline

\newline

Write your answer in simplified, rationalized form.

\newline

x =

x =

\newline

Posted 3 months ago