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Gre4nikov [31]
3 years ago
10

Consider the sequence:

Mathematics
2 answers:
Yuki888 [10]3 years ago
6 0
The given sequence is ⇒⇒⇒  <span>6, 10, 14, 18, 22, . . . .
</span>
We can note that the difference between any two consecutive terms is a constant

So, the given sequence is Arithmetic Sequence
The general rule for the the <span>arithmetic Sequence ⇒ [ a + d(n-1) ]
</span>
where a is the first term and d is the common <span>difference
</span>
For the given sequence the first term = 6 
And the common difference = 10 - 6 = 4
<span />

∴ a₃ = 6 + 4 (3 -1 ) = 14
<span />
=================================================
Another solution ( easy solution ):
a₃ ⇒⇒⇒ is the third term of the sequence and can be known directly from the given sequence which is 14

Alisiya [41]3 years ago
3 0

Answer:

The second part of the question on edg would be....

A. add 4 to the previous term to get the next term

The third part would be....

C. An= 2+4n

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Step-by-step explanation:

problem 1.

1. 6y = 30

2. y = 5

3. 3x + 2(5) = 16

4. 3x+10=16

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6. x=2

solution: (2,5)

problem 2.

1. x=7

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10x=10

x=1

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5 0
2 years ago
Help on 3. And 4. Thank you!
chubhunter [2.5K]

Answer:

#3.) The initial value of  16 gal at  x = 5 minutes means that 16 gallons of water was present 5 minutes after the barrel started leaking.

#4.) Find how many minutes until the barrel is empty of water.

Let y = 0,  to solve for time x.

0 = (-2/5)*x + 18

(2/5)*x = 18

x = (5/2)* 18 = 5*9 = 45 minutes

Up to and after 45 minutes, the barrel is empty of water.

Step-by-step explanation:

#2.)  

minutes:      5, 10, 15, 20

water(gal):  16, 14, 12, 10

Find slope:    slope m = (14 - 16)/(10 - 5) = -2/5

y - 10 = (-2/5)*(x - 20)

y - 10 = (-2/5)* x  + 8

y = (-2/5)*x + 18

rate of change slope means that for every minute  2/5 gallons of water is lost

#3.) The initial value of  16 gal at  x = 5 minutes means that 16 gallons of water was present 5 minutes after the barrel started leaking.

#4.) Find how many minutes until the barrel is empty of water.

Let y = 0,  to solve for time x.

0 = (-2/5)*x + 18

(2/5)*x = 18

x = (5/2)* 18 = 5*9 = 45 minutes

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X+(x+2)+(x+4)=396, x+x+x+6=396, 3x+6=396, 3x=396-6, 3x=390, x=130, x+2=130+2=132, x+4=130+4=134. The three consecutive even integers are 130, 132, 134
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