Question

Find an explicit function rule for the sequence -4, 1, 6, 11, .... Use the formula a(n) = a (1) + (n+1)d and simplify fully.

Answer 1

$a_1=-4\\ d=a_{n+1}-a_n\\ d=1-(-4)=1+4=5\\\\ a_n=-4+(n+1)\cdot5\\ a_n=-4+5n+5\\ a_n=5n+1$