# Given the first term and the common dimerence er an arithmetic sequence how do you find the 52nd term and the explicit formula: #a_1=-19, d=-3#?

##### 1 Answer

May 29, 2017

#### Explanation:

#"in an arithmetic sequence we can find any term using"#

#• a_n= a_1+(n-1)dlarr" nth term formula"#

#rArra_(52)=-19+(51xx-3)=-172#

#color(blue)" the explicit formula "#

#"found using the nth term formula"#

#"with " a_1=-19" and " d=-3#

#rArra_n=-19-3(n-1)#

#color(white)(xxxx)=-19-3n+3#

#color(white)(xxxx)=-3n-16larrcolor(red)" explicit formula"#

#color(blue)"As a check"#

#a_(52)=(-3xx52)-16=-172rarr" True"#