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vfiekz [6]
3 years ago
12

What is the 24th term if the arithmetic sequence where a1 = 8 and a9 = 56

Mathematics
1 answer:
AnnyKZ [126]3 years ago
5 0

Answer:

a_{24} = 146

Step-by-step explanation:

a1 = 8

a9 = 56

Using formula for finding nth term of arithmeric sequence

a_{n} =a_{1} + (n-1)d

We have to find 24th term, therefore n = 24

a_{1} is the first term but we are missing d

d is the difference between the two consecutive terms, lets calculate it first


a9 = 56

Using the above given formula for finding d

put n = 9,  a9= 56

a_{9} =a_{1}+ (9-1)d

56 = 8 + 8d

8d = 48

d = 6


Getting back to main part of finding 24th term

n = 24, d = 6, a1 = 8

put values in nth term formula

a_{n} =a_{1}+ (n-1)d

a_{24} = 8 + (24-1)6

a_{24} = 8 + 138

a_{24} = 146



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Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for the constant of integration.
trasher [3.6K]

Answer:

\frac{xe^{7x}}{7} + \frac{e^{7x}}{49}

Step-by-step explanation:

Given the integral equation

\int\limits{xe^{7x}} \, dx \\

According to integration by part;

\int\limits {u} \, dv = uv +  \int\limits {v} \, du

u = x, dv = e^7x

du/dx = 1

du = dx

v = \int\limits {e^{7x}} \, dx \\v = e^7x/7

Substitute the given values into the formula;

\int\limits {xe^{7x}} \, dx = x(e^{7x}/7) + \int\limits ({e^{7x}/7}) \, dx\\\int\limits {xe^{7x}} \, dx = \frac{xe^{7x}}{7} + \frac{e^{7x}}{7*7} \\\int\limits {xe^{7x}} \, dx = \frac{xe^{7x}}{7} + \frac{e^{7x}}{49}

3 0
3 years ago
I don’t understand what to do with this one
earnstyle [38]

Answer:

1 2/3

Step-by-step explanation:

Change the mixed number to an improper fraction

5 5/6 = (6*5+5)/6 = 35/6

Multiply the improper fraction by the fraction

5 5/6 * 2/7

35/6 * 2/7

70/42

Divide the top and bottom by 14

5/3

Changing back to a mixed number

3/3 +2/3

1 2/3

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The length of 7 (the minor arc) is 15 cm. What is the circumference of Z?
Firlakuza [10]

Answer:450 cm

Step-by-step explanation:

5 0
3 years ago
Plzzzzzz HELPPP ASPPPP Select the correct answer.
gayaneshka [121]
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6 0
3 years ago
2. There are some benches in a classroom. If 4 students sit on each bench then 3 benches
NARA [144]

Answer: There are 48 students in the class.

Step-by-step explanation:

Let the number of students = S

Let the number of benches = B

<em>If 4 students sit on each bench, 3 benches are left vacant.</em>

S = 4(B - 3)

S = 4·B - 12 } Equation 1

<em>If 3 students sit on each bench, 3 students still standing.</em>

S = 3·B + 3 } Equation 2

We can match the two equations because they both indicate the same number of students.

4B - 12 = 3·B + 3

on solving this

4·B - 3·B = 3 + 12

B = 15 → number of benches

That is the number of benches, therefore substituting the value for B in equation 1

S = 4·B - 12 Equation 1

S = 4·15 -12

S = 60 - 12 = 48 → number of students

Answer: There are 48 students in the class.

<h3>Verification</h3>

There are 48 students and 15 benches.

<em>If 4 students sit on each bench, 3 benches are left vacant.</em>

48students ÷ 4students/bench = 12 benches are occupied and left 3 vacant benches.

<em>If 3 students sit on each bench, 3 students still standing.</em>

<h3 />

15benches * 3 students/bench = 45 students are sitting and 3 students remain standing.

<h3>Checked!!</h3>

\textit{\textbf{Spymore}}​​​​​​

8 0
3 years ago
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