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Zigmanuir [339]
3 years ago
14

Foe the AP given by a1,a2,......,an,...with non zero common difference, the equation satisfied are

Mathematics
1 answer:
user100 [1]3 years ago
8 0
The given sequence is
a₁, a₂, ..., a_{n}

Because the given sequence is an arithmetic progression (AP), the equation satisfied is
a_{n}=a_{1}+(n-1)d
where
d =  the common difference.

The common difference may be determined as
d = a₂ - a₁

The common difference is the difference between successive terms, therefore
d = a₃ - a₂ = a₄ - a₃, and so on..

The sum of the first n terms is
S_{n}= \frac{n}{2} (a_{1}+a_{n})

Example:
For the arithmetic sequence
1,3,5, ..., 
the common difference is d= 3 - 1 = 2.
The n-th term is
a_{n}=1+2(n-1)

For example, the 10-term is
a₁₀ = 1 + (10-1)*2 = 19
Th sum of th first 10 terms is
S₁₀ = (10/2)*(1 + 19) = 100



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The original price of a skateboard was $85. The owner of the store
lora16 [44]

Answer:

\$68

Step-by-step explanation:

1. Approach

To solve this problem, one wants to find the price of a product after its discount has been applied. The discount is 20% off, so the new price of the item is 80% of its original price (percent is out of 100 so if a an item is 20% off, it is 100 - 20 = 80; 80% the original price). To calculate the percent cost, one would divide the percent value by 100, and then multiply it by the price of the item.

2. Solving

The price of the new item is 80% of the price of the original item.  To calculate the percent cost, cent, one would divide the percent value by 100, and then multiply it by the price of the item.

Therefore, the equation that will be formed is,

price * \frac{percent}{100}

Substitute,

85 * \frac{80}{100}

Simplify,

85 * 0.8\\\\= 68

5 0
3 years ago
Create a table and graph y=x+1 demos<br>​
DerKrebs [107]

Answer:

The table will be:

x          y=x+1

1            2

2           3

3           4

4           5

5           6

The graph is shown in figure attached.

Step-by-step explanation:

We need to create table and graph the expression: y=x+1

Table is made, such that we take value of x and find value of y

You can take any values of x from negative values to positive values. I am taking values of x: 1,2,3,4,5 and find value of y.

So our table will be:

x          y=x+1

1            2

2           3

3           4

4           5

5           6

Now, we will plot these value on the graph. x values will be on x-axis and corresponding y-values will be on y-axis.

The graph is shown in figure attached.

8 0
3 years ago
Mario’s company makes unusually shaped imitation gemstones. One gemstone had 10 faces and 12 vertices. How many edges did the ge
Evgen [1.6K]
20 edges 
F=12, V=10
V -E+F=2
10-E+12=2
-E+22=2
-E=-20
E=20
8 0
4 years ago
Read 2 more answers
There are 60 animal exhibits at the local zoo. What percent of the zoo's exhibits does each animal class represent?​
snow_lady [41]

Answer:

30+15+12+3=  60

for mammal 30/60=0.50%

reptile 15/60=0.25%

fish  12/60= 0.20%

bird 3/60=0-05%

i hope that helps

8 0
3 years ago
Hi I need to find DO length ​
MakcuM [25]

Answer:

10 cm

Step-by-step explanation:

If we assume that DC is parallel to AB, then triangle DOC is similar to triangle AOB.

However, even with this assumption, there is not enough information in the diagram to solve for DO.  We would also need to know the length of CO.  Then we could write a proportion:

DO / (DO + 20) = CO / (CO + 24)

Edit: OD is 2 cm shorter than OC.  If we call x the length of OD, then the length of OC is x+2.

Putting this into our proportion:

x / (x + 20) = (x + 2) / (x + 2 + 24)

x / (x + 20) = (x + 2) / (x + 26)

Cross multiply:

x (x + 26) = (x + 2) (x + 20)

Distribute:

x² + 26x = x² + 20x + 2x + 40

x² + 26x = x² + 22x + 40

4x = 40

x = 10

So the length of DO is 10 cm.

4 0
3 years ago
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