Fill in the blank. Through any two points there is/are exactly ___

If this particular arithmetic sequence, a7=34 and a15=74. What is the value of a21

Ilya [14]

This is an arithmetic sequence, meaning, to get the next term, you simply add some value to the current one, namely the "common difference" "d".

now, we know the 17th term is 34, let's go to the 15term then

34 + d
34 + d + d
34 + d + d + d
34 + d + d + d + d
34 + d + d + d + d + d
34 + d + d + d + d + d + d
34 + d + d + d + d + d + d + d
34 + d + d + d + d + d + d + d + d

now, notice, we got to the 15th term, which is 34 + d + d + d + d + d + d + d + d, or namely 34 + 8d, it just so happen we know is 74, therefore,

$\bf 34+8d=74\implies 8d=40\implies d=\cfrac{40}{8}\implies \boxed{d=5}$

ok, now that we know what the common difference is, let's find the first term in the sequence using the 7th term of 34,

$\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
n=7\\
d=5\\
a_7=34
\end{cases}
\\\\\\
a_7=a_1+(7-1)5\implies 34=a_1+(7-1)5
\\\\\\
34=a_1+30\implies \boxed{4=a_1}$

and now let's use those 2 found folks, to get the 21st term,

$\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
a_1=4\\
d=5\\
n=21
\end{cases}
\\\\\\
a_{21}=4+(21-1)5\implies a_{21}=4+100\implies a_{21}=104$

3 0

3 years ago

Lightfoot Inc., a software development firm, has stock outstanding as follows: 30,000 shares of cumulative preferred 2% stock, $

Lesechka [4]

The calculation of the dividends per share on each class of stock for each of the four years for Lightfoot Inc. are:

1st Year 2nd Year 3rd Year 4th Year

Preferred stock $0.19 $0.32 $0.99 $0.50

Common stock $0 $0 $0.79 $2.69

How is dividend per share calculated?

The dividend per share for each class of stock can be computed by dividing the total dividend distributed by the number of shares outstanding.

For cumulative preferred stock, the unpaid dividends in a year are carried forward for distribution when profits are made. Note also that preferred stock dividends enjoy preferential payment before common stock dividends.

<h3>Data and Calculations:</h3>

Cumulative preferred stock = 30,000 shares

Par value of preferred stock = $25

Dividend rate = 2%

The total value of preferred stock = $750,000 ($25 x 30,000)

Expected annual dividend for preferred stockholders = $15,000 ($750,000 x 2%)

Common stock = 38,000 shares

Par value of common stock = $75

The total value of ordinary stock = $2,850,000 ($75 x 38,000)

<h3>Dividends distribution:</h3>

1st Year 2nd Year 3rd Year 4th Year

Dividends distributed $5,700 $9,600 $59,720 $117,220

Preferred stock $5,700 $9,600 $29,700 $15,000

Preferred stock per share $0.19 $0.32 $0.99 $0.50 ($15,000/30,000)

Common stock $0 $0 $30,020 $102,220

Common stock per share $0 $0 $0.79 $2.69 ($102,220/38,000)

Thus, the dividends distribution of Lightfoot Inc. shows that the common stockholders started earning dividends after the second year.

Learn more about cumulative preferred stock dividends at brainly.com/question/14006397

#SPJ1

<h3>Question Completion:</h3>

Calculate the dividends per share on each class of stock for each of the four years. Round all answers to two decimal places. If no dividends are paid in a given year, enter "O."

6 0

2 years ago

Simplify the expression:<br><br> 2(3 + g) =

Alex17521 [72]

Answer:

6 + 2g

Step-by-step explanation:

whenever you have a problem like that you have to distribute the 2 to both the numbers in the parenthesis. You have to multiply 2 by 3 which is 6. Then you multiply 2 by g and you get 2g. We can't get any further so the simplified expression would be 6 + 2g

4 0

3 years ago

Solve the problem. Check answers to be sure they are reasonable.

eimsori [14]

Answer:

8

Step-by-step explanation:

4 0

3 years ago

Write down a pair of integers whose sum is –3

inysia [295]

The pair is any numbers, 1 positive and one negative, that add up to -3.
Here is a sample;
(-5, 2)

7 0

3 years ago

Read 2 more answers

Fill in the blank. Through any two points there is/are exactly ____ line(s).