I am doing Geometric sequences, but I cannot figure out how to find the Nth term of a geometric sequence.

The problem is A1 = 64, Ak+1 = 1/2Ak
(That is supposed to be A sub one, A sub k + 1, etc.)

The formula for finding the equation is:

An = A1 x R^n-1

The answer is:

An = 128(1/2)^n

I cannot figure out what to do and what happens to the n-1 and how it gets to just n.

Help is greatly appreciated. Thanks.

To find the nth term of a geometric sequence, you can use the formula An = A1 x R^(n-1), where An represents the nth term, A1 is the first term of the sequence, R is the common ratio, and n is the position of the term you want to find.

Let's apply this formula to the given problem. We have A1 = 64, and the given recursive formula is Ak+1 = (1/2)Ak.

To start, we need to find the common ratio (R) from the recursive formula. Notice that in your sequence, each term is half of the previous term. As a result, the common ratio (R) is (1/2).

Now, substitute the known values into the formula An = A1 x R^(n-1):

An = 64 x (1/2)^(n-1)

To simplify further, let's rewrite (1/2)^(n-1) as (1/2)^n x (1/2)^(-1):

An = 64 x (1/2)^n x (1/2)^(-1)

Using the property of exponents, (1/2)^(-1) is equal to 2, so we can rewrite the equation as:

An = 64 x (1/2)^n x 2

Finally, we can simplify (1/2)^n x 2 as (1/2)^n-1:

An = 128 x (1/2)^n

Hence, the formula to find the nth term of the given geometric sequence is:

An = 128 x (1/2)^n, where n represents the position of the term you want to find.

Therefore, in this particular sequence, the nth term is given by An = 128 x (1/2)^n.