Question

A(1)=20
a(n)=a(n−1)*(2/3)
what is the 3rd term in the sequence?

Answer 1

To find the 3rd term in the sequence, we use the given recursive formula starting with the 2nd term calculated from the first term which is 20. Multiplying by 2/3 for each step, the 2nd term becomes 40/3, and then the 3rd term is 80/9 or approximately 8.89.

Step-by-step explanation:

The question provided is asking for the 3rd term in a given recursive sequence. The first term a(1) is given as 20, and each subsequent term is found by multiplying the previous term by 2/3.

To find the 3rd term in the sequence, a(3), we will apply the recursive formula twice starting from the first term:

1. a(2) = a(1) × (2/3) = 20 × (2/3) = 40/3 or approximately 13.33
2. a(3) = a(2) × (2/3) = (40/3) × (2/3) = 80/9 or approximately 8.89

Therefore, the 3rd term in the sequence is a(3) = 80/9 or approximately 8.89.