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katrin2010 [14]
3 years ago
11

Consider the sequence {4,6,8,10,...} find the 130th term of the sequence

Mathematics
1 answer:
Olin [163]3 years ago
3 0

262

Step-by-step explanation:

Step 1:

To find the nth term of a sequence the basic formula is

Sn = (n*d) + (a-d)

Whereas

Sn= nth Term

n= Term to be found

d= Difference between the terms in the sequence

a= First term in the sequence

Step 2:

Sn = (130*2) +(4-2)

= 260+2

Sn= 262

The nth term for the given problem is 262

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Answer:   v = -3

=========================================

Work Shown:

5 = \sqrt{-2-6v}+1\\\\5-1 = \sqrt{-2-6v}\\\\4 = \sqrt{-2-6v}\\\\4^2 = \left(\sqrt{-2-6v}\right)^2 \ \text{ .... square both sides}\\\\16 = -2-6v\\\\16+2 = -6v\\\\18 = -6v\\\\-6v = 18\\\\v = 18 \div (-6)\\\\v = -3

As you can see, we don't square both sides until the square root portion is fully isolated or on its own side. So it happens after we subtract 1 from both sides.

Technically, you are able to square both sides without first isolating the square root. But that would mean you'd have to use the FOIL rule and things would get a bit messier than they have to be. Not to mention that the square root term wouldn't fully go away (so you'd have to square again later down the line).

------------------

Checking the answer:

Replace every copy of v with -3. Simplify both sides. We should end up with the same number on each side

5 = \sqrt{-2-6v}+1\\\\5 = \sqrt{-2-6(-3)}+1\\\\5 = \sqrt{-2+18}+1\\\\5 = \sqrt{16}+1\\\\5 = 4+1\\\\5 = 5\\\\

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