# How do you find nth term rule for #1,-6,36,-216,...#?

##### 1 Answer

Aug 23, 2017

#### Explanation:

#"these represent the terms in a geometric sequence."#

#a,ar,ar^2,ar^3,......,ar^(n-1)#

#"where a represents the first term and r the common ratio"#

#r=a_2/a_1=a_3/a_2=....=a_n/a_(n-1)#

#"here "r=(-6)/1=36/(-6)=(-216)/36=-6#

#"the nth term is calculated using "#

#•color(white)(x)a_n=ar^(n-1)=1xx(-6)^(n-1)=(-6)^(n-1)#