MATHEMATICS HIGH SCHOOL

Please help with sequences and series problem!

Answers

Answer 1

Answer:

In an arithmetic sequence, consecutive terms are separated by a common difference $d$ and are given recursively by

$a_n=a_(n-1)+d$

So we can write $a_(51)$ in terms of $a_(11)$ by substituting recursively:

$a_(51)=a_(50)+d$

$a_(51)=(a_(49)+d)+d=a_(49)+2d$

$a_(51)=(a_(48)+d)+2d=a_(48)+3d$

and so on up to

$a_(51)=a_(11)+40d$

(notice how in $a_x+yd$ , it's always true that $x$ and $y$ add up to 51)

We're given that $a_(11)=23$ and $a_(51)=183$ , so we can solve for $d$ :

$183=23+40d\implies40d=160\implies d=40$

We can use the same strategy to find the first term in the sequence:

$a_(11)=a_(10)+40$

$a_(11)=(a_9+40)+40=a_9+80$

$a_(11)=(a_8+40)+80=a_8+120$

and so on up to

$a_(11)=a_1+400$

$23=a_1+400\implies a_1=-377$

In general, the sequence has a pattern of

$a_n=a_(n-1)+40$

$a_n=(a_(n-2)+40)+40=a_(n-2)+2\cdot40$

$a_n=(a_(n-3)+40)+2\cdot40=a_(n-3)+3\cdot40$

and so on up to

$a_n=a_1+(n-1)\cdot40$

So this sequence is given by the rule

$a_n=-377+40(n-1)\implies \boxed{a_n=40n-417}$

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Which set of integers is included in (-1,3]?

Answers

the answer could be 0 , 1 , 2 , 3 hope this helps!

What is the value of 8C5?

A.56

B.6720

C.960

D.40

Answers

Using, binomial coefficient, the value of 8C5 is 56, which corresponds to option A.

To calculate the value of 8C5 (8 choose 5), we use the binomial coefficient formula:

nCr = n! / (r! * (n - r)!)

where n is the total number of items, r is the number of items chosen.

In this case, n = 8 and r = 5.

8C5 = 8! / (5! * (8 - 5)!)

Now, let's calculate the factorials:

8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320

5! = 5 * 4 * 3 * 2 * 1 = 120

3! = 3 * 2 * 1 = 6

Now, substitute these values back into the formula:

8C5 = 40,320 / (120 * 6)

8C5 = 40,320 / 720

8C5 = 56

Therefore, the value of 8C5 is 56, which corresponds to option A.

To know more about binomial coefficient:

brainly.com/question/34713364

#SPJ6

Answer: The answer would be 56!

Step-by-step explanation:

6x7x8 / 3! =56

In a dilation, the ratio of the length of a side on the image to the length of its corresponding side on the pre-image is called the___ ___A) Center of dilation
B) Scale factor
C) Expansion or contraction
D) Mapping rule

Plssss help im stuck on this and correct only please for brainliest

Answers

it B i took the pre test

Which expression correctly represents “three less than the product of a number and two, increased by five”?

Answers

Answer:

Let x represents the number.

Given the statement: "Three less than the product of a number and two, increased by five".

"Product" means multiply

"Product of a number and two" translated to $2x$

"Three less than the product of a number and two" translated to 2x - 3

Increased by 5 means +5

then;

the given statement becomes;

$(2x-3)+5$

Therefore, the expression that represents "three less than the product of a number and two, increased by five" is $(2x-3)+5$

Answer: 3 - (2n+5)

Step-by-step explanation:

I think so.

If it isn't tell me so I can fix it :D

Find the measure of the arc indicatedA. 144

B. 150

C. 130

D. 131

Answers

Answer:

I need to see the picture

Step-by-step explanation:

(10y^3+20y^2+55y)/5y

Answers

( 10y^3 + 20y^2 +55y ) / 5y
= 2y^2 + 4y +11

And then depending on if the equation is set to zero in the problem, just factor or use the quadratic formula on the quadratic equation that is left.

Answer:

2y^2+4y+11

Step-by-step explanation:

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