Question

question 4 points 2

if the first term of a geometric sequence is \\(\frac{1}{4}\\) and the common ratio is 2, then find the third term using the recursive method.

1

\\(\frac{1}{4}\\)

Explanation:

Identify given parameters

We are given the first term \(a_1 = \frac{1}{4}\) and the common ratio \(r = 2\) of a geometric sequence.

Define recursive formula

A geometric sequence can be defined recursively by relating each term to the previous term:

$$a_n = r \cdot a_{n-1} \quad \text{for } n \ge 2$$

Calculate the second term

Using the recursive relation for \(n = 2\):

$$a_2 = r \cdot a_1 = 2 \cdot \frac{1}{4} = \frac{1}{2}$$

Calculate the third term

Using the recursive relation for \(n = 3\):

$$a_3 = r \cdot a_2 = 2 \cdot \frac{1}{2} = 1$$

Answer:

• (A) 1 (Correct answer)
• (B) 1/4