Find a formula for the n'th of the sequence :

2,4,8,16,32

Hint: the sequence is:

21,22,23,24,25,...

To find a formula for the n'th term of a sequence, we need to look for a pattern or relationship between the terms. In this case, let's examine the given sequence:

2, 4, 8, 16, 32

From the given sequence, we can observe that each term is obtained by multiplying the previous term by 2. In other words, each term is double the value of the previous term.

So, the formula for the n'th term of the sequence can be determined as follows:

n'th term = first term * (common ratio)^(n-1)

In this case:

first term = 2 (the first term of the sequence)
common ratio = 2 (the factor by which each term is multiplied to get the next term)

Therefore, the formula for the n'th term of the given sequence is:

n'th term = 2 * 2^(n-1)

You can use this formula to find the n'th term for any value of n in the given sequence.