Question

Find the 100th term in the arithmetic sequence

-19,-14,-9,-4,1...
a.
100
c.
476
b.
471
d.
481


Please select the best answer from the choices provided

A
B
C
D

Answer 1

$a_n=a_1+(n-1)d\\\\d=a_{n+1}-a_n$

$a_1=-19;\ a_2=-14;\ a_3=-9;\ a_4=-4;\ a_5=1;\ ...\\\\d=a_2-a_1=a_3-a_2=a_4-a_3=...\\\\d=-14-(-19)=-14+19=5\\\\a_n=-19+(n-1)(5)=-19+5n-5=5n-24\\\\a_{100}=5(100)-24=500-24=476\to\boxed{c.}$