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

Sep 1, 2016

$d = 8$

#### Explanation:

Write a systems of equations, with respect to $d$ and ${t}_{3}$.

${t}_{3} - d + {t}_{3} + d = 30$

${t}_{3} + \left({t}_{3} - 2 d\right) = 14$

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

$2 {t}_{3} = 30$

${t}_{3} = 15$

Substituting into the second equation:

$15 + 15 - 2 d = 14$

$30 - 2 d = 14$

$- 2 d = - 16$

$d = 8$

Hopefully this helps!

Sep 1, 2016

$d = 8$

#### 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 $a , a + d , a + 2 d , a + 3 d$. Hence as first and third term add up to $14$ and second and fourth term add upto $30$,,

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

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

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

Hence series is $\left\{- 1 , 7 , 15 , 23\right\}$