Question

Determine x so that x, 1/2x+7, and 3x-1 are the first three terms of an arithmethic sequence?

Answer 1

Common difference between the terms must be equal, therefore

`t_2 -t_1 = t_3 - t_2`

`1/2x +7 -x = 3x-1-(1/2x +7)`

`-1/2x + 7 = 3x - 1 - 1/2x - 7`

`15 =3x`

`x=5`

We can confirm by plugging in `5` for `x` to see that the terms of the sequence are `5, 19/2, 14` which do indeed for an arithmetic sequence.

Hopefully this helps!