Explanation:
64
,
32
,
16 \
,
8
,
4
is a geometric sequence.
this is a sequence where, to get from one term to the next, there is a number that you have to multiply it by. this is the same for all parts of the sequence.
64
2
=
32
32
2
=
16
etc.
to get from
64
to
32
, you divide by
2
.
this is the same as multiplying by
1
2
64
⋅
1
2
=
64
1
⋅
1
2
=
64
2
=
32
hence, the number that each term is multiplied by to find the next is
1
2
.
if we call one term
a
n
and the previous term
a
n
−
1
, where
n
shows position in the sequence and therefore that
a
n
is one ahead of
a
n
−
1
, then we find that
a
n
=
1
2
a
n
−
1
.
this is the notation for the term-to-term rule, using
n
for the current position,
n
−
1
for the position before, and
a
n
with
a
n
−
1
to show progress from one position to the next.
