Question

Write the first five terms of the geometric sequence with the given values.

a_3=4, r=2
a_1=__

Answer 1

To find the first term (a1) of the geometric sequence, use the formula a_n = a1 * r^(n-1). Plug in the given values and solve for a1.

Step-by-step explanation:

To find the first term (a1) of the geometric sequence, we can use the formula an = a1 * r^(n-1), where an is any term of the sequence, a1 is the first term, and r is the common ratio.

In this case, we are given a3 = 4 and r = 2. Plugging these values into the formula, we get:

4 = a1 * 2^(3-1)

Simplifying this equation, we find:

4 = 4a1

Dividing both sides of the equation by 4, we find:

a1 = 1

Therefore, the first term of the geometric sequence is a1 = 1.