Convert the recursive form a1 = 5, = 2an-1 to the explicit form

Answer 1

To convert the recursive form a1 = 5, an = 2an-1 to the explicit form, we need to find a formula that directly gives us the value of each term in the sequence without relying on previous terms.

Let's begin by examining the first few terms of the sequence:

a1 = 5
a2 = 2a1 = 2(5) = 10
a3 = 2a2 = 2(10) = 20
a4 = 2a3 = 2(20) = 40

We can observe that each term is double the previous term. So, we can express the relationship between the terms as:

an = 2^(n-1) * a1

Substituting the given value a1 = 5, we have:

an = 2^(n-1) * 5

Therefore, the explicit form of the sequence is:

an = 5 * 2^(n-1)