Find the 100th term to 1,3,9,27​

The n-th term of this sequence appears to be

3

n

−

1

,

n

≥

1

.

Step-by-step explanation:

These are powers of

3

ordered from

3

0

=

1

to

3

a

(for an integer

a

≥

1

). However, the first convenient value for

n

is

1

, not

0

(imagine saying the 0th term of a sequence). Because of that, since the first term is actually

3

0

, we need to start from the first term (

n

=

1

) being

3

1

−

1

. The next is

3

2

−

1

,

3

3

−

1

...

3

n

−

1

.