The nth term, an, of an arithmetic sequence can be defined recursively by _____ for n≠1.(1 point)
Responses
an−1+d
A subscript n minus 1 baseline plus d
an−1−d
A subscript n minus 1 baseline minus d
a1+dn
A subscript 1 baseline plus d n
a1+d(n−1)
A subscript 1 baseline plus d(n−1)
Tn+1 = Tn+ d
Yes, the correct recursive definition for the nth term of an arithmetic sequence would be:
an = an-1 + d for n ≠ 1
So the nth term, an, is equal to the previous term, an-1, plus the common difference, d.
or
Tn = Tn-1 + d
unless n = 1
Yes, that is also a correct way to define the nth term of an arithmetic sequence recursively. It is written as:
Tn = Tn-1 + d for n ≠ 1
This equation states that the nth term is equal to the previous term plus the common difference, d, unless n is equal to 1.