All categories

2 years ago

The first term of an arithmetic sequence is 1 and the sum of the first four terms is 100. Find the first four terms

Mathematics

2 answers:

vampirchik [111]2 years ago

8 0

Answer:

see the file attached!!!!

7nadin3 [17]2 years ago

3 0

Answer:

1, 17, 33, 49

Step-by-step explanation:

given the first term is 1 then the next 3 terms are

1 + d, 1 + 2d, 1 + 3d ( d is the common difference )

the sum of the first 4 terms is 100 , then

1 + 1 + d + 1 + 2d + 1 + 3d = 100 , that is

4 + 6d = 100 ( subtract 4 from both sides )

6d = 96 ( divide both sides by 6 )

d = 16

1 + d = 1 + 16 = 17

1 + 2d = 1 + 2(16) = 1 + 32 = 33

1 + 3d = 1 + 3(16) = 1 + 48 = 49

the first 4 terms are

1, 17, 33, 49

You might be interested in

Match each set of vertices with the type of quadrilateral they form.

Serjik [45]

Only correct the first one.

Please, see the graph in the attached file.

1) a rectangle with    A(3,3), B(3,6),
noncongruent ←→ C(7,6), D(7,3)
adjacent sides
(in green)

2) a parallelogram
with A(2,0), B(3,2)
nonperpendicular ←→ C(6,3), D(5,1)
adjacent sides
(in blue)

3) a square ←→ A(3,3), B(2,5),
(in red) C(4,6), D(5,4)

4) a rhombus with       A(2,-2), B(3,0),
nonperpendicular    ←→ C(4,-2), D(3,-4)
adjacent sides
(in black)

5 0

4 years ago

Graph the solution on the number line |x-3| <5

Anettt [7]

Answer:

-2<x<8

see below for graph

Step-by-step explanation:

First, we need to solve the inequality.

Inequality: |x-3|<5

Split into two equations:

x-3<5

x-3>-5 (notice how the sign is flipped when we make the number negative)

let's start with x-3<5

add 3 to both sides

x<8

now

x-3>-5

add 3 to both sides

x>-2

The graph is below

the intersection is the solution.

Notice how I made the maroon line go to the right- which shows that it's greater than (for x>-2) and the silver line go to the left, which shows that it's less than (for x<8)

the equation is -2<x<8

Hope this helps!

8 0

3 years ago

Polygon ABCD is translated to create polygon A'B'C'D. Point A and is located at (1, 5) and point A' is located at (-2, 1). What

Ilia_Sergeevich [38]

$\sqrt{ 3^{2}+4^{2} } =5.$
the distance is 5.
hope it helps.

7 0

3 years ago

SSHA scores Here are the scores on the Survey of Study Habits and Attitudes (SSHA) for 18 first-year college women:154 109 137 1

mihalych1998 [28]

Answer:

Women has better study habit than men.

Step-by-step explanation:

For knowing who has better study habits and attitudes toward learning we have to find the mean of both the women and men data.

The first step is that we only take first 18 values of both women(X) and men(Y) data, to make them of same length

Mean is used to measure the central tendency of data which represents the whole data in the best way. It can be found as the ratio of the sum of all the observations to the total number of observations.

Calculating all values:

$\bar{X}$ = 141.0556

$\bar{Y}$ = 121.25

Thus, women has better study habit than men. Since Mean of X is larger than Mean of Y.

5 0

3 years ago

Pavel, Ruth and Josh have part-time jobs.

MrMuchimi

M+m+z/3=3m
m+m+z=9m
2m+z=9m
z=7m
m+m+7m/3=3m
9m=9m
m=1
1+1+z/3=3
2+z=9
z=7
idk but i think that one person gets paid 7 dollars and the other ppl get paid 1 dollar----- this is probably veryyyyy wrong

8 0

3 years ago

The first term of an arithmetic sequence is 1 and the sum of the first four terms is 100. Find the first four terms ​

The first term of an arithmetic sequence is 1 and the sum of the first four terms is 100. Find the first four terms