# What is the 20th term of the arithmetic sequence 5, -1, -7, ?

Jul 27, 2015

=a_20=color(blue)(-109

#### Explanation:

The arithmetic sequence is
$5 , - 1 , - 7$

The common difference $d$ of this sequence is
$d = - 1 - 5 = - 6$

The formula for ${n}_{t h}$ of an arithmetic series is:
color(blue)(a_n = a+(n-1)(d)

Here, $a = 5 , d = - 6 , n = 20$

So,  a_20 = 5 +19(-6)

$= 5 - 114$
=color(blue)(-109