Question

Given two terms in the geometric sequence, find the explicit formula. a^4 = -1/4 and a^1 = -2.

Answer 1

To find the explicit formula of a geometric sequence, divide any term by the previous term to find the common ratio. Then use the formula a_n = a_1 * r^(n-1) to find the nth term.

Step-by-step explanation:

To find the explicit formula of a geometric sequence given two terms, we need to find the common ratio (r). We can do this by dividing any term (a_n) by the previous term (a_{n-1}). In this case, we can divide a^4 by a^1 to get:

a^4 / a^1 = -1/4 / -2 = 1/8.

So, the common ratio (r) is 1/8.

Now we can use the formula for the nth term of a geometric sequence:

a_n = a_1 * r^(n-1).

Plugging in the values, we get:

a_n = -2 * (1/8)^(n-1).