All categories

1 year ago

The sum of the first four terms of an arithmetic sequence is $10$. If the fifth term is $5$, what is the sixth term?

Mathematics

1 answer:

Nookie1986 [14]1 year ago

7 0

The sixth term of an arithmetic sequence is 6

<h3>How to find arithmetic sequence?</h3>

The sum of the first four terms of an arithmetic sequence is 10.

The fifth term is 5.

Therefore,

sum of term = n / 2(2a + (n - 1)d)

where

a = first term
d = common difference
n = number of terms

Therefore,

n = 4

10 = 4 / 2 (2a + 3d)

10 = 2(2a + 3d)

10 = 4a + 6d

4a + 6d = 10

a + 4d = 5

4a + 6d = 10

4a + 16d = 20

10d = 10

d = 1

a + 4(1) = 5

a = 1

Therefore,

6th term = a + 5d

6th term = 1 + 5(1)

6th term = 6

learn more on sequence here: brainly.com/question/24128922

#SPJ1

You might be interested in

What is the value of x if f(x) = 76

GaryK [48]

Answer:

The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace f(x) with 0 and solve for x

No solution

3 0

3 years ago

What is the value of x in the equation below?

sveta [45]

Answer: C

Step-by-step explanation:

1+2e^x+1=9

2e^x+1=9-1

e^x+1= 8/2

e^x+1 = 4

Here we can applicate the Ln:

ln e^x+1 = ln 4

Applicating the log property for exponent:

(x+1).ln e = ln 4

Ln e = 1, so:

x+1 = ln 4

x = ln 4-1

7 0

3 years ago

If the area of a square with side x is equal to the area of a triangle with base x, then find the altitude of the triangle.

zhannawk [14.2K]

Answer:

$h= 2x$

Step-by-step explanation:

Given

Square

$Side = x$

Triangle

$Base = x$

$Altitude = h$

Required

Find h, if both shapes have the same area

The area of the square is:

$Area = x * x$

$Area = x^2$

The area of the triangle is:

$Area = \frac{1}{2} * Base*Height$

$Area = \frac{1}{2} * x*h$

Equate both areas

$x^2 = \frac{1}{2} * x*h$

Divide both sides by x

$x = \frac{1}{2} *h$

Multiply both sides by 2

$2*x = \frac{1}{2} *h*2$

$2x = h$

$h= 2x$

3 0

2 years ago

In which pair of numbers is the first number a multiple of the second number?

Sedaia [141]

Answer:

27,9

Step-by-step explanation:

9x3=27

5 0

3 years ago

Sally is planning a trip for 225 students.

sdas [7]

Answer:

Number of students want to go to Theme Park = 75

Step-by-step explanation:

Note: The given question is incomplete. Complete question is as follow.

Given:

Number of sample student = 30

Place Number of students want to go

Theme Park 10

Theater 5

Sports Center 8

Seaside 7

Find:

How many students want to go to Theme Park.

Computation:

⇒ Probability for students want to go to Theme Park = 10 / 30

⇒ Probability for students want to go to Theme Park = 1 / 3

⇒ Number of students want to go to Theme Park = [1 / 3]225

⇒ Number of students want to go to Theme Park = 75

3 0

2 years ago