The sequence you’ve presented is 2, 4, 8, 16, 32. To find the general term of this sequence, we first need to identify the pattern between the numbers.
Each term in the sequence is obtained by multiplying the previous term by 2:
- 2 × 2 = 4
- 4 × 2 = 8
- 8 × 2 = 16
- 16 × 2 = 32
This indicates that the sequence is a geometric progression where the first term (a) is 2 and the common ratio (r) is also 2.
The general formula for the nth term of a geometric sequence can be expressed as:
T(n) = a × r^(n – 1)
Substituting the values we have:
T(n) = 2 × 2^(n – 1)
Therefore, the general term for the sequence can be written as:
T(n) = 2^n
In conclusion, the general term for the sequence 2, 4, 8, 16, 32 is 2^n, where n starts from 1 (for 2) and continues onwards (2^1 = 2, 2^2 = 4, 2^3 = 8, etc.).