Question

1. a satellite program launches 5 satellites in its first year. in the following years, the number of satellites launched follows the pattern 10, 20, 40. write a recursive equation for this pattern.

Explanation:

Step1: Identify the pattern

The sequence is \(10, 20, 40,\cdots\). We can see that each term is obtained by multiplying the previous term by \(2\).

Step2: Write the recursive formula

Let \(a_n\) be the number of satellites launched in the \(n\) -th year. The first - year launch \(a_1 = 10\).
For \(n\geq2\), the recursive formula is \(a_n=2a_{n - 1}\)

Answer:

The recursive formula is \(a_1 = 10\) and \(a_n=2a_{n - 1}\) for \(n\geq2\)