# How do you write the first five terms of the arithmetic sequence given a_8=26, a_12=42?

Aug 8, 2018

$- 2 , 2 , 6 , 10 , 14$

#### Explanation:

The general term of an arithmetic sequence is given by the formula:

${a}_{n} = a + d \left(n - 1\right)$

where $a$ is the initial term and $d$ the common difference.

Given ${a}_{8} = 26$ and ${a}_{12} = 42$, we find:

$16 = 42 - 26$

$\textcolor{w h i t e}{16} = {a}_{12} - {a}_{8}$

$\textcolor{w h i t e}{16} = \left(a + 11 d\right) - \left(a + 7 d\right)$

$\textcolor{w h i t e}{16} = 4 d$

Hence $d = 4$

Then:

$26 = {a}_{8} = a + 7 d = a + 28$

Hence $a = - 2$

So the first five terms of the sequence are:

$- 2 , 2 , 6 , 10 , 14$