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Cloud [144]
4 years ago
5

Calculate the arithmetic sequence in which a9=17 and the common difference is d=-2.1

Mathematics
2 answers:
jek_recluse [69]4 years ago
8 0

Answer:

S_{31}=71.3


Step-by-step explanation:

The nth term of an arithmetic sequence is given by the formula,

U_n=a_1+(n-1)d


We were given that the 9th term is 17.


\Rightarrow 17=a_1+(9-1)(-2.1)


\Rightarrow 17=a_1+(8)\times(-2.1)


\Rightarrow 17=a_1-\frac{84}{5}


\Rightarrow 17+\frac{84}{5}=a_1


\Rightarrow a_1=\frac{169}{5}


The sum of the first n-terms is given by the formula,


S_n=\frac{n}{2}(2a_1+(n-1)d)


To find S_{31}, we substitute n=31, a_1=\frac{169}{5} and d=-2.1.


\Rightarrow S_{31}=\frac{31}{2}(2(\frac{169}{5}+(31-1)(-2.1))


\Rightarrow S_{31}=\frac{31}{2}(2(\frac{169}{5}+(30)(-2.1))



\Rightarrow S_{31}=\frac{31}{2}(\frac{23}{5})


\Rightarrow S_{31}=\frac{713}{10}


\Rightarrow S_{31}=71.3


The correct answer is D















sladkih [1.3K]4 years ago
7 0

Answer:

The correct answer is d-71.3

Step-by-step explanation:

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7.4.PS-6
Sedaia [141]

Answer:

The area of the given polygon is:

  • <u>232 cm^2</u>

Step-by-step explanation:

To find the area of the polygon in the picture, you can divide the polygon in three rectangles: a 3 cm by 14 cm, a 5 cm by 14 cm rectangle, and the last rectangle must have a base of 12 cm (20 cm - 3 cm - 5 cm), and a height of 10 cm (14 cm - 4 cm). We can calculate the area of the rectangles with the formula below:

  • Area of a rectangle = Base * height

Now, we're gonna replace the measurements in the formula.

<em>First rectangle:</em>

  • Area of a rectangle = 3 cm * 14 cm
  • <u>Area of a rectangle = 42 cm^2</u>

<em>Second rectangle:</em>

  • Area of a rectangle = 5 cm * 14 cm
  • <u>Area of a rectangle = 70 cm^2</u>

<em>Third rectangle:</em>

  • Area of a rectangle = 12 cm * 10 cm
  • <u>Area of a rectangle = 120 cm^2</u>

By last, we must add the area of the rectangles:

  • Area of the polygon = 42 cm^2 + 70 cm^2 + 120 cm^2
  • <u>Area of the polygon = 232 cm^2</u>

As you can see, <em><u>the area of the polygon in the picture is 232 cm^2</u></em>.

5 0
3 years ago
What do I do on this?
stiks02 [169]
All you do is measure it with a ruler and for every 1 cm you get multiply it by 8.5ft. 
so for example if you got 6cm then you would multiply it by 8.5ft and your answer would be 51ft.
4 0
3 years ago
7.25 cm plus 7.2 cm plus 8cm equals what
alisha [4.7K]
There correct answer to that question is 22.45
7 0
4 years ago
Read 2 more answers
0m0 Hello and bye also good evening
Salsk061 [2.6K]

Answer:

15/32

Step-by-step explanation:

5/8 ÷ 1 1/3

Change to an improper fraction

5/8 ÷ ( 3*1+1)/3

5/8 ÷ 4/3

Copy dot flip

5/8 * 3/4

15/32

5 0
4 years ago
3/4 divided into 2/3 equals (in the kcf method)
Darina [25.2K]

Answer:

a

Step-by-step explanation:

8 0
3 years ago
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