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Reil [10]
2 years ago
8

What is the value of a3 in the sequence?

Mathematics
2 answers:
Studentka2010 [4]2 years ago
7 0
Basically, we are trying to find the third number in the pattern. The pattern is - -4, -2, -12, -14 and so on. We can see that the third number is -12, which is a₃. Therefore, the answer is C) -12. Hope this helped!
nika2105 [10]2 years ago
6 0

Answer:

C.)-12

Step-by-step explanation:

A sequence is an ordered list of numbers.

One way to define the sequence is by listing the numbers of the sequence.

This list is

a1,a2,a3,a4,a5, ... ,an

Where a1 is the first number of the sequence, a2 is the second number of the sequence , ... , an is the ''nth'' number of the sequence meaning that the sequence has a total of ''n'' numbers.

In this exercise, the sequence is

-4,-2,-12,-14,...

This means that the first number of the sequence is -4 ⇒ a1 = -4

The second number is -2 ⇒ a2 = -2

The third number is -12 ⇒ a3 = -12

The value of a3 in the sequence is -12

The correct option is C.)-12

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Solve the following congruence equations for X a) 8x = 1(mod 13) b) 8x = 4(mod 13) c) 99x = 5(mod 13)
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Answer:

a) 5+13k  where k is integer

b) 20+13k where k is integer

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Step-by-step explanation:

(a)

8x \equiv 1 (mod 13) \text{ means } 8x-1=13k.

8x-1=13k

Subtract 13k on both sides:

8x-13k-1=0

Add 1 on both sides:

8x-13k=1

I'm going to use Euclidean Algorithm.

13=8(1)+5

8=5(1)+3

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Now backwards through the equations:

3-2=1

3-(5-3)=1

3-5+3=1

(8-5)-5+(8-5)=1

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5(8)-3(13)=1

So compare this to:

8x-13k=1

We see that x is 5 while k is 3.

Anyways 5 is a solution or 5+13k is a solution where k is an integer.

b)

8x \equiv 4 (mod 13)

8x-4=13k

Subtract 13k on both sides:

8x-13k-4=0

Add 4 on both sides:

8x-13k=4

We got this from above:

5(8)-3(13)=1

If we multiply both sides by 4 we get:

8(20)-13(12)=4

So x=20 and 20+13k is also a solution where k is an integer.

c)

[tex]99x \equiv 5 (mod 13)[/tex

99x-5=13k

Subtract 13k on both sides:

99x-13k-5=0

Add 5 on both sides:

99x-13k=5

Using Euclidean Algorithm:

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13=8(1)+5

Go back through the equations:

13-8=5

13-(99-13(7))=5

8(13)-99=5

99(-1)+8(13)=5

Compare this to 99x-13k=5 and see that x=-1 or -1+13=12 or 12+13k is a solution where k is an integer.

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