Question

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`?

Answer 1

`a_(52)=-172, a_n=-3n-16`

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"`