Question

How do you write the expression for the nth term of the geometric sequence `a_1=4, r=1/2, n=10`?

Answer 1

See the explanation below.

Explanation:

The equation for a geometric sequence is `a_n = a_1 (r)^(n-1)`, where `a_n` is the `n^(th)` term, `a_1` is the first term, and `r` is the common ratio.

We can substitute the given values into the equation.

`a_10 = 4(1/2)^(10-1)`

`a_10 = 4(1/2)^(9)`

`a_10 = 4(1/512)`

`a_10 = 1/128`