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?
Let's first calculate `x`.
Since difference between two consecutive terms is 4 it follows
So first three terms are: 4, `3cdot4-4=8`, `4+8=12`
On the other hand we have
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
So fifth element is `a_5=x+4cdotd=4+4cdot4=20`