### Home > A2C > Chapter 5 > Lesson 5.2.1 > Problem5-70

5-70.

Consider the arithmetic sequence $2$, $a − b$, $a + b$, $−35$, … Find $a$ and $b$.

Since this sequence is arithmetic, what has to be true about the differences between terms?

How many times would you add the difference to get from 2 to 35?

$2 + d + d + d = 35$

$d = 11$

Since you know the first term and the common difference, you can write all four terms of the sequence.

Use the sequence to write a system of equations: $a − b = ?$ and $a + b = ?$

$a = 18.5, b = 5.5$