If you were asked to find the 87th term in a sequence, which formula would you want to be given?

1 answer:

3 0

To determine the nth term of sequence, first we need to know what type of sequence is it. It can be an arithmetic sequence or a geometric sequence. For an arithmetic sequence, the nth can be determined by the formula,

an = a1 + (n-1)d

For a geometric sequence,

an = a1r^n-1

Hope this answers the question.

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X^5 + 243 divided by x+3

ch4aika [34]

-3   | 1   0   0   0   0   243 $\longleftarrow$ coefficients of the polynomial you're dividing
.     |                                   $\longleftarrow$ drop down the leading coefficient
- - - - - - - - - - - - - - - - - - -
.     | 1

On the left side of the frame, we write -3 because we're dividing by $x+3=x-(-3)$ . (The algorithm is followed for division of a polynomial by a factor of $x-c$ .) Since we're dividing a degree 5 polynomial by a degree 1 polynomial, we expect to get a degree 4 polynomial.

-3   | 1   0   0   0   0   243
.     |      -3                         $\longleftarrow$ multiply -3 by 1, write in next column, add to 0
- - - - - - - - - - - - - - - - - - -
.     | 1 -3

Repeat step for the remaining columns.

-3   | 1   0   0   0   0   243
.     |      -3   9
- - - - - - - - - - - - - - - - - - -
.     | 1 -3   9

-3   | 1   0   0      0   0   243
.     |      -3   9   -27
- - - - - - - - - - - - - - - - - - -
.     | 1 -3   9   -27

-3   | 1   0   0      0 0   243
.     |      -3   9   -27   81
- - - - - - - - - - - - - - - - - - - - -
.     | 1 -3   9   -27   81

-3   | 1   0   0      0 0 243
.     |      -3   9   -27   81 -243
- - - - - - - - - - - - - - - - - - - - -
.     | 1 -3   9   -27   81       0

which translates to

$\dfrac{x^5+243}{x+3}=x^4-3x^3+9x^2-27x+81$

So the bottom row of the frame gives the coefficients of each term in the quotient by descending order. Since the last coefficient is 0, this means the remainder upon division vanishes, i.e. $x^5+243$ is exactly divisible by $x+3$ .

- - -

Another way to get the same result is to use a well-known result: for $a+b\neq0$ ,

$a^5+b^5=(a+b)(a^4-a^3b+a^2b^2-ab^3+b^4)\implies\dfrac{a^5+b^5}{a+b}=a^4-a^3b+a^2b^2-ab^3+b^4$

and in this case $a=x$ and $b=3$

3 0

4 years ago

Three workers worked for 5 hours, 7 hours and 12 hours. The total wage of $

BARSIC [14]

Answer:

Worked 5 hours: $550

Worked 7 hours: $2,750

Worked 12 hours: $6,600

Step-by-step explanation:

5+7+12=24

13200/24 = 550

(5)*(550) = 2,750

(7)*(550) = 3,850

(12)*(550) = 6,600

5 0

3 years ago

The concession stand at a ballpark makes $0.43 profit from each hot dog sold. It also makes a profit of $0.65 from each pretzel

kaheart [24]

0.43h + 0.65p + 1.31d = c

explanation:
h stands for hotdogs, p for pretzels, and d for drinks. c represents the total cost.
each price next to the variable describes the profit per item.

hope this helps! :D

4 0

3 years ago

Read 2 more answers

What is the order of rotational symmetry for the figure?

mylen [45]

C is the right answer.

Trust me char!!

Na bakla na yswa!

7 0

2 years ago

I need help understanding this ASAP PLZ!!!!

MAXImum [283]