SOLUTION

The given sequence is a geometric progression where each term is obtained by multiplying the previous term by 2.

Identifying the Sequence

The first few terms of the progression are:

– 1st term: $ 2^1 = 2 $

– 2nd term: $ 2^2 = 4 $

– 3rd term: $ 2^3 = 8 $

In general, the $ n $-th term of this geometric progression can be expressed as:

$a_n = 2^n$

Finding the 51st Term

To find the 51st term $ a_{51} $:

$a_{51} = 2^{51}$

Conclusion

Thus, the 51st term of the progression is  $ 2^{51} $.