Question

What is the term-to-term rule for this sequence? 64, 32, 16, 8,4

Answer 1

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.