If  given `x, 3x-4, x+8,ldots`   and the first term `x` and the difference between any two consecutive terms is 4.

Name the  value of the fifth term in the sequence?

Expert Answers

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Let's first calculate `x`.

Since difference between two consecutive terms is 4  it follows

`3x-4-x=4`

`2x=8=> x=4`

So first three terms are: 4, `3cdot4-4=8`, `4+8=12`

On the other hand we have

`x-3x+4=4=>x=0` 

So the first three terms would be: 0, `3cdot0-4=-4`, `0+8=0` but here we see that difference between third and second term is not 4, so `x=0` si not our solution.

This is an arithmetic sequence and as such it is defined by first element of the sequance `a_1` ( that is `x=4` in your case) and difference `d`  (in your case that's 4).

`n`th element of arithmetic sequence is defined by formula

`a_n=a_1+(n-1)d`

So fifth element is `a_5=x+4cdotd=4+4cdot4=20`

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