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3 years ago

Find an explicit formula for the arithmetic sequence -5,13,31,49

Mathematics

1 answer:

Keith_Richards [23]3 years ago

4 0

an explicit formula for the arithmetic sequence -5,13,31,49 is $a_n =18n-23$ .

Step-by-step explanation:

Here we have an arithmetic sequence -5,13,31,49 . We need to find an explicit formula for the arithmetic sequence .Let's find out:

Let $a_1 = -5 , a_2=13 ,a_3=31,a_4=49$ be terms of an A.P , common difference is :

⇒ $d=a_2-a_1$

⇒ $d=13-(-5)$

⇒ $d=13+5$

⇒ $d=18$

We know that general term of an Arithmetic Progression ( A.P) is :

⇒ $a_n = a+(n-1)d$

So , Here we will have $a_n = -5+(n-1)18$

⇒ $a_n = -5+(n-1)18$

⇒ $a_n = -5+18n-18$

⇒ $a_n =18n-23$

Therefore , an explicit formula for the arithmetic sequence -5,13,31,49 is $a_n =18n-23$ .

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WITCHER [35]

Answer:

A≈166.28cm²

Step-by-step explanation:

Using the formulas

A=33

2a2

P=6a

A=3P2

24=3·482

24≈166.27688cm²

3 0

3 years ago

WILL MARK BRAINLIEST!!! 40 POINTS!! ACTUAL ANSWERS, PLZZZ

steposvetlana [31]

Answer:

Part A:

$\left(x + 7\right)^{5}=x^{5} + 35 x^{4} + 490 x^{3} + 3430 x^{2} + 12005 x + 16807$

Part B:

The closure property describes cases when mathematical operations are CLOSED. It means that if you apply certain mathematical operations in a polynomial it will still be a polynomial. Polynomials are closed for sum, subtraction, and multiplication.

It means:

$\text{Sum of polynomials } \Rightarrow \text{ It will always be a polynomial}$

$\text{Subtraction of polynomials } \Rightarrow \text{ It will always be a polynomial}$

$\text{Multiplication of polynomials } \Rightarrow \text{ It will always be a polynomial}$

But when it is about division:

$\text{Division of polynomials } \Rightarrow \text{ It will not always/sometimes be a polynomial}$

Example of subtraction of polynomials:

$(2x^2+2x+3) - (x^2+5x+2)$

$x^2-3x+1$

Step-by-step explanation:

First, it is very important to define what is a polynomial in standard form:

It is when the terms are ordered from the highest degree to the lowest degree.

Therefore I can give:

$x^5-5x^4+3x^3-3x^2+7x+20$

but,

$x^5+3x^3-3x^2+7x+20-5x^4$ is not in standard form.

For this question, I can simply give the answer: $x^5-5x^4+3x^3-3x^2+7x+20$ and it is correct.

But I will create a fifth-degree polynomial using this formula

$(a+b)^n=\sum_{k=0}^n \binom{n}{k} a^{n-k} b^k$

Also, note that

$\binom{n}{k}=\frac{n!}{(n-k)!k!}$

For $a=x \text{ and } b=7$

$\left(x + 7\right)^{5}=\sum_{k=0}^{5} \binom{5}{k} \left(x\right)^{5-k} \left(7\right)^k$

$\text{Solving for } k \text{ values: } 0, 1, 2, 3, 4 \text{ and } 5$

Sorry but I will not type every step for each value of $k$

The first one is enough.

For $k=0$

$\binom{5}{0} \left(x\right)^{5-0} \left(7\right)^{0}=\frac{5!}{(5-0)! 0!}\left(x\right)^{5} \left(7\right)^{0}=\frac{5!}{5!} \cdot x^5= x^{5}$

Doing that for $k$ values:

$\left(x + 7\right)^{5}=x^{5} + 35 x^{4} + 490 x^{3} + 3430 x^{2} + 12005 x + 16807$

8 0

3 years ago

The points (5,7) and (25,35) form a proportional relationship. Find the slope of the line through the

weqwewe [10]

Answer:

7/5 ( y= $\frac{7}{5}$ x )

Step-by-step explanation:

To find the slope, you can use this formula: $\frac{y_{2}-y_{1} }{x_{2} -x_{1} }$ which equals $\frac{35-7}{25-5}$ If we subtract, we get $\frac{28}{20}$ . We can simplify it down to $\frac{7}{5}$ which is the answer. :)