An arithmetic sequence is defined by the recursive formula t1 = -30, tn + 1 = tn - 4, where n ∈N and n ≥ 1. Which is the general term of the sequence?
A)
tn = -30 - 4n, where n ∈N and n ≥ 1
B)
tn = -30 + 4n, where n ∈N and n ≥ 1
C)
tn = -26 - 4n, where n ∈N and n ≥ 1
D)
tn = -26 + 4n, where n ∈N and n ≥ 1

Question

An arithmetic sequence is defined by the recursive formula t1 = -30, tn + 1 = tn - 4, where n ∈N and n ≥ 1. Which is the general term of the sequence?
A)
tn = -30 - 4n, where n ∈N and n ≥ 1
B)
tn = -30 + 4n, where n ∈N and n ≥ 1
C)
tn = -26 - 4n, where n ∈N and n ≥ 1
D)
tn = -26 + 4n, where n ∈N and n ≥ 1

amoodarya · Answer

t2=t1-4
so t2=-30-4=-34
so d=-4
t(n)=t1 +(n-1)d
t(n)=-30 +(n-1)(-4)
    =-30-4n +4
so t(n)=-26-4n  for all n>=1