Convert the recursive form a1=5,an=2an-1 to the explicit form.
To convert the recursive form a1=5, an=2an-1 to the explicit form, we need to find a general expression for the term an in terms of n.
Let's examine the pattern of the terms:
a1 = 5 (given)
a2 = 2a1 = 2*5 = 10
a3 = 2a2 = 2*10 = 20
a4 = 2a3 = 2*20 = 40
...
From the pattern, we can see that the terms are doubling with each consecutive term. So, we can express the nth term as:
an = 5*2^(n-1)
Therefore, the explicit form of the recursive sequence is an = 5*2^(n-1).