New Notations
A recursive formula expresses each new term of a sequence based on the preceding term in
the sequence. The recursive formulas to determine the nth term of an arithmetic sequence and a
geometric sequence are shown.
Arithmetic Sequence
common
difference
nth
term
Geometric Sequence
common
ratio
nth
term
an 5 an 2 1 1 d
gn 5 gn 2 1 ? r
previous
term
previous
term
The explicit formula represents the sequence as a function. The explicit formulas to determine
the nth term of an algebraic sequence and a geometric sequence are shown.
Arithmetic Sequence
common
difference
© Carnegie Learning, Inc.
nth
term
an 5 a1 1 d(n 2 1)
1st
term
previous
term number
Geometric Sequence
nth
term
previous
term number
gn 5 g1 ? r n 2 1
1st
term
common
ratio
TOPIC 2: Sequences • M1-79E