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ahrayia [7]
2 years ago
7

Write the rule for the nth term of each sequence.

Mathematics
1 answer:
stira [4]2 years ago
8 0

Rule for sequence a is: a_n = 10-3n

Rule for sequence b is: a_n = -19+8n

Step-by-step explanation:

a.)7, 4, 1, -2, ...

First of all we have to find the common difference. Common difference is the difference between consecutive terms of an arithmetic sequence

Here,

a_1 = 7\\a_2 = 4\\a_3 = 1\\d = a_2 - a_1 = 4-7 = -3\\d = a_3 - a_2 = 1-4 = -3

The explicit rule for an arithmetic sequence is:

a_n = a_1 + (n-1)d

Putting the value of a1 and d

a_n = 7 + (n-1)(-3)\\a_n = 7 -3n+3\\a_n = 10-3n

b.)-11, -3, 5, 13, ...

First of all we have to find the common difference. Common difference is the difference between consecutive terms of an arithmetic sequence

Here,

a_1 = -11\\a_2 = -3\\a_3 = 5\\d = a_2 - a_1 = -3+11 = 8\\d = a_3 - a_2 = 5+3 = 8

The explicit rule for an arithmetic sequence is:

a_n = a_1 + (n-1)d

Putting the value of a1 and d

a_n =-11 + (n-1)(8)\\a_n = -11 +8n-8\\a_n = -19+8n

Hence,

Rule for sequence a is: a_n = 10-3n

Rule for sequence b is: a_n = -19+8n

Keywords: Arithmetic sequence, common difference

Learn more about arithmetic sequence at:

  • brainly.com/question/2048256
  • brainly.com/question/2115122

#LearnwithBrainly

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The width of a rectangle is 6 kilometers less than twice its length. if its area is 108 square​ kilometers, find the dimensions
Art [367]
Hi there!

Answer:
length = 9 kilometres
Width = 12 kilometres

Let's solve this problem step by step!
To find our answer we need to set up and solve an equation.

Let the length of the rectangle be represented by x.
The width of the rectangle can therefore be expressed by 2x - 6.

The area of a rectangle can be found by using the formula:
A = width × length

Plug in the data from the formula
A = x (2x - 6).

Simplify using rainbow technique.
x(2x - 6) = 2 {x}^{2} - 6x

Now we've found the simplified expression that expresses the area of the rectangle. Therefore, we can now set up and start solve the equation.

2 {x}^{2} - 6x = 108
Subtract 108

2 {x}^{2} - 6x - 108 = 0
Divide by 2.

{x}^{2} - 3x - 54
(x - 9)(x + 6) = 0
Rule AB = 0, gives A is 0 or B is 0.

x - 9 = 0 \\ x = 9 \\ \\ x + 6 = 0 \\ x = - 6

The length of the rectangle, which was represented by x, must be 9 (since it cannot be a negative number).

Length
x = 9
Width
2x - 6 = 2 \times 9- 6 = 18 - 6 = 12

Answer:
length = 9 kilometres
Width = 12 kilometres

~ Hope this helps you!
6 0
3 years ago
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