What is the formula for the nth term for the example 6, 12, 24, 48, 96?

To find the formula for the nth term of the sequence
6
,
12
,
24
,
48
,
96
6,12,24,48,96, we can observe that each term is obtained by multiplying the previous term by 2. This suggests that the sequence follows a geometric progression.

In general, a geometric progression has the form
,
,
2
,
3
,
4
,
…
a,ar,ar
2
,ar
3
,ar
4
,…, where 'a' is the first term and 'r' is the common ratio between consecutive terms.

In the given sequence, the first term 'a' is 6, and the common ratio 'r' is 2 (since each term is obtained by multiplying the previous term by 2).

Therefore, the formula for the nth term of this sequence can be written as:
=
×
(
−
1
)
T
n
​
=a×r
(n−1)


Substituting the values 'a = 6' and 'r = 2' into the formula, we get:

=
6
×
2
(
−
1
)
T
n
​
=6×2
(n−1)


So, the formula for the nth term of the sequence
6
,
12
,
24
,
48
,
96
6,12,24,48,96 is
=
6
×
2
(
−
1
)
T
n
​
=6×2
(n−1)
.