Question

State the first 5 terms of the geometric sequence with a=24 and r=(1)/(3)

Answer 1

The first 5 terms of the geometric sequence with an initial term of 24 and a common ratio of 1/3 are 24, 8, approximately 2.6667, approximately 0.8889, and approximately 0.2963.

Step-by-step explanation:

The student has asked for the first 5 terms of the geometric sequence with an initial term a equal to 24 and a common ratio r of ⅓. The terms of a geometric sequence are found by multiplying the previous term by the common ratio. Thus, the sequence can be represented as a, a*r, a*r^2, a*r^3, a*r^4.

Using the given values, the first term (a) is 24. We can then calculate the subsequent terms as follows:

1. The second term is a*r = 24 * ⅓ = 8
2. The third term is a*r^2 = 24 * (⅓)^2 = 8 * ⅓ ≈ 2.6667
3. The fourth term is a*r^3 = 24 * (⅓)^3 = 8 * (⅓)^2 ≈ 0.8889
4. The fifth term is a*r^4 = 24 * (⅓)^4 = 8 * (⅓)^3 ≈ 0.2963

Therefore, the first 5 terms of the geometric sequence are 24, 8, 2.6667, 0.8889, and 0.2963.