# How do you find the first five terms of the sequence a_1=7, a_(n+1)=a_n-2?

Sep 18, 2017

$\left\{7 , 5 , 3 , 1 , - 1\right\}$

#### Explanation:

We have:

$\left\{\begin{matrix}{a}_{1} & = 7 \\ {a}_{n + 1} & = {a}_{n} - 2\end{matrix}\right.$

Put $n = 1$

${a}_{2} = {a}_{1} - 2$
$\setminus \setminus \setminus \setminus = 7 - 2$
$\setminus \setminus \setminus \setminus = 5$

Put $n = 2$

${a}_{3} = {a}_{2} - 2$
$\setminus \setminus \setminus \setminus = 5 - 2$
$\setminus \setminus \setminus \setminus = 3$

Put $n = 3$

${a}_{4} = {a}_{3} - 2$
$\setminus \setminus \setminus \setminus = 3 - 2$
$\setminus \setminus \setminus \setminus = 1$

Put $n = 4$

${a}_{5} = {a}_{4} - 2$
$\setminus \setminus \setminus \setminus = 1$
$\setminus \setminus \setminus \setminus = - 1$

Hence, the first five terms of the sequence are:

$\left\{{a}_{1} , {a}_{2} , {a}_{3} , {a}_{4} , {a}_{5}\right\} = \left\{7 , 5 , 3 , 1 , - 1\right\}$