Write an explict formula for the sequence 7,2,-3,-8,-13
we have
a1=7
a2=2
a3=-3
a4=-8
a5=-13
Find the commom difference d
d=a2-a1=2-7=-5
d=a3-a2=-3-2=-5
d=a4-a3=-8-(-3)=-5
d=a5-a4=-13-(-8)=-5
so
d=-5
In this problem we have an artithmetic sequence
so
an=a1+d(n-1)
we have
a1=7
d=-5
substitute
an=7+(-5)(n-1)
an=7-5n+5
an=12-5n
therefore
the answer is
an=12-5n