1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Paul [167]
3 years ago
14

What is the nth term?

Mathematics
1 answer:
kumpel [21]3 years ago
7 0

Let a_k denote the <em>k</em>th term of the sequence. Then

a_k=a_1+d(k-1)

where <em>d</em> is the common difference between consecutive terms in the sequence and <em>a</em>₁ is the first term.

The sum of the first <em>n</em> terms is

S_n=\displaystyle\sum_{k=1}^na_k=a_1+a_2+\cdots+a_{n-1}+a_n

From the formula for a_k, we get

S_n=\displaystyle\sum_{k=1}^n(a_1+d(k-1))=a_1\sum_{k=1}^n1+d\sum_{k=1}^n(k-1)

S_n=\displaystyle na_1+d\sum_{k=0}^{n-1}k

S_n=na_1+\dfrac{d(n-1)n}2

S_n=\dfrac n2(2a_1-d+dn)

So we have d=-5, and 2a_1-d=16 so that a_1=\frac{11}2.

Then the <em>n</em>th term in the sequence is

a_n=\dfrac{11}2-5(n-1)=\boxed{\dfrac{21-10n}2}

You might be interested in
Please help, please help
zmey [24]
Answers:
x=22
x+4=26
6x=132

Explanation:
We learned from the question that all of the angles in a triangle add up to 180 degrees.

180=angle+angle+angle

When we plug in the values that the question gives us for the angles, we get this equation:

180=x+6x+(x+4)

After solving this equation, we get 22 as the value of x (The process of solving that equation is in the picture attached).

To solve for (x+4), we plug in the value of x, which is 22 and add 4.

(x+4)
=(22+4)
=26

And finally, to solve for 6x, we plug in 22 again:

6x
=6*22
=132

Hope this helps!

7 0
3 years ago
A water wheel has a radius of 4 feet and the bottom of the wheel is 1 foot from the ground. one plank is painted white and it st
Sliva [168]

The correct option is 9 feet.

The height from the ground the white plank after the motion is 9 feet.

<h3>What is rotational motion?</h3>

Anything that spins or moves in a circular route is said to be in rotational motion. It's also referred to as angular motion and circular motion. The motion can be uniform (— in other words, the velocity v remains constant) and non-uniform, but it must be circular.

Now, according to the question;

The wheel's radius is 4 feet.

The height of a bottom of a wheel from the ground equals 1 foot.

π/3 radians is the angle where the wheel is rolled.

The following relationship describes the height of a revolving wheel.

f(t) = A·sin(B·t + C) + D

Where,

D = Mid line =  4 + 1 = 5 feet

B·t = π/3

C = 0

amplitude; A = 4

Substituting the values in the function;

f(t) = 4×sin(π/3) + 5 = 8.464 ft

f(t) = 9 (approx)

Therefore, the plank's height after the /3π/3 rotation motion = 9 ft.

To know more about the rotational motion, here

brainly.com/question/2136775

#SPJ4

3 0
2 years ago
Which representation of a transformation on a coordinate grid does not preserve congruence?
Ghella [55]
The second one time for me a little kid I got the wrong thing to say I was
6 0
2 years ago
What is the vertex of the graph of y + 2x + 3 = –(x + 2)2 + 1? (–3, –33) (–3, 3) (3, –24) (3, 21)
Arte-miy333 [17]
ANSWER

(-3,3)

EXPLANATION

The given function is

y + 2x + 3 = - (x + 2) ^{2} + 1

Expand

y + 2x + 3 = - x ^{2} - 4x - 4 + 1

Rewrite in the form:

y =a {x}^{2} + bx + c

This implies that,

y = - x ^{2} - 4x - 2 x - 4 + 1 - 3

y = - {x}^{2} - 6x - 6

Complete the square to get,

y = - ( {x}^{2} + 6x) - 6

y = - ( {x}^{2} + 6x + {(3)}^{2} ) - - {(3)}^{2} - 6

y = - {(x + 3)}^{2} +9 - 6

y = - {(x + 3)}^{2} +3

The function is now in the form:

y = a {(x - h)}^{2} +k

where (h,k) =(-3,3) is the vertex
8 0
3 years ago
Read 2 more answers
Gil charges $5 per bracelet plus $2 for each string colour. If Gil makes 3 bracelets
hichkok12 [17]

Answer: 15 + 2x

Step-by-step explanation:

5b + 2x

5 (3) + 2x

15 + 2x

I think I'm right so I hope it helped!!

8 0
2 years ago
Read 2 more answers
Other questions:
  • Miss Holman gave a 90-cent tip to a waitress for serving a meal costing $6.00. What percent of the bill was her tip?
    11·1 answer
  • What type of number is 9 1/2?
    11·2 answers
  • What is a the gcf of 8
    10·2 answers
  • Help ASAP please! Really am struggling with this topic
    15·2 answers
  • Determine two coterminal angles (one positive and one negative) for the angle - 361".​
    14·1 answer
  • Find the length of side a ​
    12·2 answers
  • Change each fraction to higher terms 1/5=?/10
    12·1 answer
  • What is the length of leg s of the triangle below?
    15·1 answer
  • Help meeeeeeeeeeeeeeeeeeeeee​
    14·1 answer
  • ABC= ADC, BA= 25, DA=
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!