All categories

4 years ago

The sum of the first 200 terms of the arithmetic sequence with initial term 2 and common difference 3 is

Mathematics

1 answer:

Svetradugi [14.3K]4 years ago

8 0

Answer: D. 60100

Step-by-step explanation:

The formula for determining the sum of n terms of an arithmetic sequence is expressed as

Sn = n/2[2a + (n - 1)d]

Where

n represents the number of terms in the arithmetic sequence.

d represents the common difference of the terms in the arithmetic sequence.

a represents the first term of the arithmetic sequence.

From the information given,

n = 200 terms

a = 2

d = 3

Therefore, the sum of the first 200 terms, S200 would be

S200 = 200/2[2 × 2 + (200 - 1)3]

S200 = 100[4 + 597)

S200 = 100 × 601 = 60100

You might be interested in

Visual Description for Figure 1

just olya [345]

The slope in question seven is 1. Below are the solutions to the remaining questions

<h3>In what means can Transformation occur ?</h3>

Transformation of an object can occur in different ways. Such as translation, rotation, enlargement of different scale factors, reflection and dilation.

Given that Blue points, blue line segments, red points, and red line segments arranged on a Cartesian coordinate plane. Here are the blue points and their coordinates. Point A: (negative nine, 3). Point B: (negative 11, 3). Point C: (negative 10, 3). Point D: (negative 10, 5). Point F: (negative 10, 4). Point E: (negative 11, 4). Here are the red points and their coordinates. Point A-1: (negative 1, 6). Point A-2: (negative 3, 4). Point B-1: (negative 2, 4). Point B-2: (negative 5, 4). Point C-2: (negative 3, 3). Point D-1: (negative 5, 5). Point D-2: (negative 5, 3). Point E-1: (negative 6, 6). Point F-1: (negative 5, 6). A semicircle that lies below its line of symmetry AB. A semicircle that lies above its line of symmetry B-2 A-2. A triangle DEF. A triangle D-1 E-1 F-1. Line segments are drawn from C to D, from A-1 to B-1, from A-2 to B-2, and from C-2 to D-2. Triangle DEF, segment CD, and the semicircle with line of symmetry BA are arranged so that they look like a boat.

1. The transformations to use on the blue segment CD to get it to match with the red segment C2D2 is ROTATION of 180° Clockwise

2.The transformations to use on the blue triangle to get it to match with the red triangle is ROTATION of 360° Clockwise Explain your movement using the coordinates of the vertices.

3.The line segments on the boat that is parallel is line B2 to A2 because it is parallel to line D2 to C2

4.The line segments on the boat is perpendicular is line BCA because they are perpendicular to line CFD and AB.

5.The line segments on the boat have a slope of 0 is line BCA because change in y axis is 0

6.The line segments on the boat have an undefined slope is line DFC because change in x axis is 0. When denominator is zero, the fraction is undefined.

7.Given that E is at (−11,4) and D is at (−10,5), the slope of ED will be

Slope = Δy ÷ Δx

Slope = (5 - 4) ÷ (-10 + 11)

Slope = 1 ÷ 1

Slope = 1

Learn more about Transformation here: brainly.com/question/1462871

#SPJ1

8 0

2 years ago

What value of c makes the polynomial below a perfect square?

malfutka [58]

Answer:

Step-by-step explanation:

x² + 9x

to complete the square

add ( half the coefficient of the x- term )² to x² + 9x

= x² + 2( $\frac{9}{2}$ )x + ( $\frac{9}{2}$ )²

= x² + 9x + $\frac{81}{4}$ ← the value of c

= (x + $\frac{9}{2}$ )² ← a perfect square

6 0

3 years ago

Read 2 more answers

In the bronze medal game of the 2014 FIBA Asia Cup, and with his team down by two points, Philippines guard Paul Dalistan was fo

dsp73

Complete Question

Question: In the bronze medal game of the 2014 FIBA Asia Cup... In the bronze medal game of the 2014 FIBA Asia Cup, and with his team down by two points, Philippines guard Paul Dalistan was fouled while attempting a three-pointer at the buzzer. He missed the shot and headed to the line for three foul shots.

1. Watch the video of Dalistan preparing to take his first shot. Before he shoots, what is the probability that Philippines will win the game? Lose the game? Send it into overtime? Dalistan’s free throw percentage is 84.6%

Answer:

The probability that Philippines will win the game is $P(A) = 0.6055$

The probability that Philippines will lose the game is $P(B) = 0.00365$

The probability that the game will be sent to overtime is $P(C) = 0.06$

Step-by-step explanation:

From the question we are told that

The probability of Paul Dalistan making a shot is p = 0.846

The probability of Paul Dalistan not making the shot is $q = 1- p = 1- 0.846=0.154$

Paul Dalistan team was down by two points

This mean that for Paul Dalistan's team to win the game he must make the 3 free throws

So the probability that Philippines will win the game is mathematically represented as

$P(A) = p^3$

=> $P(A) = 0.846^3$

=> $P(A) = 0.6055$

Gnerally for Paul Dalistan's team to loss the game it means that Paul Dalistan did not make any of the free shot

Hence the probability that Philippines will loss the game is

$P(B) = q^3$

=> $P(B) = (0.154 )^3$

=> $P(B) = 0.00365$

Generally for the game to be sent to overtime then the game must be tied and for the game to be tied, Paul Dalistan have to make 2 out of the three shots

Hence the probability that game will go to overtime is

$P(C) = 3 * 0.846 * 0.154 * 0.154$

$P(C) = 0.06$

6 0

4 years ago

The marketing department of a sports supply store wants to estimate the percentage of adults in the town who belong to a gym.

velikii [3]

A) If you only sample people in a sports supply store, your sample will be biased. People in a sports supply store are more likely to be people that belong to a gym.
B) While it does not have necessarily the same amount of bias as sampling people in the sports supply store, people that go to a park are generally more likely to be people that exercise or have a gym membership.
C) Taking a random sample of people in town is a good way to get a non-biased sample. They are not necessarily predisposed to answer your question one way or another.
D) For the same reason as choice A, this is a biased sample.

C is the best choice.

4 0

3 years ago

Hometown Grocery, Inc. has 50 comma 000 shares of common stock outstanding and 4 comma 000 shares of preferred stock outstandin

Anit [1.1K]

Answer:

$0.36 per share

Step-by-step explanation:

The data provided in the question are as follows

Common stock outstanding = 50,000 shares

Preferred stock outstanding = 4,000 shares

Par value of common stock = $4

Interest rate and par value of preferred stock = 9% and $100

Total dividend payment declared = $54,000

So, the amount of dividend for each share of common stock is

= (Total dividend payment declared - Preferred stock outstanding × interest rate × par value) ÷ (common stock outstanding)

= ($54,000 - 4,000 × $100 × 9%) ÷ (50,000 shares)

= ($54,000 - $36,000) ÷ (50,000 shares)

= $18,000 ÷ 50,000 shares

= $0.36 per share

7 0

3 years ago