Question

If the first and third terms equal to 14 and the second and fourth terms equal to 30, what is d?

Answer 1

`d = 8`

Explanation:

Write a systems of equations, with respect to `d` and `t_3`.

`t_3 - d + t_3 + d = 30`

`t_3 + (t_3 - 2d) =14`

However, when we look at the first equation, we realize a system wasn't necessary. The d's cancel out to give the following:

`2t_3 = 30`

`t_3 = 15`

Substituting into the second equation:

`15 + 15 - 2d = 14`

`30 - 2d = 14`

`-2d = -16`

`d = 8`

Hopefully this helps!

Answer 2

`d=8`

Explanation:

Although it is not mentioned, as questioner has mentioned `d`, it is apparent that he is talking about arithmetic sequence with common difference `d`.

Let the numbers be `a, a+d, a+2d, a+3d`. Hence as first and third term add up to `14` and second and fourth term add upto `30`,,

`a+a+2d=14` i.e. `2a+2d=14` and `a+d+a+3d=30` i.e. `2a+4d=30`.

Subtracting first from second equation, we get `2d=16` or `d=8` and putting this in first we get

`2a+16=14` i.e. `2a=-2` and `a=-1`.

Hence series is `{-1,7,15,23}`