Question



Find the fifth term of the following recursive function. Show all work using the recursive function.
=
A of 0 = 2.5, a of n a of n-1+ 3.2

Answer 1

To find the fifth term of the recursive function, we need to recursively calculate each term leading up to the fifth term. The recursive formula is given by a of n = a of n-1 + 3.2.

Starting from n = 1:
a of 1 = a of 0 + 3.2
a of 1 = 2.5 + 3.2
a of 1 = 5.7

Now, for n = 2:
a of 2 = a of 1 + 3.2
a of 2 = 5.7 + 3.2
a of 2 = 8.9

Next, for n = 3:
a of 3 = a of 2 + 3.2
a of 3 = 8.9 + 3.2
a of 3 = 12.1

Moving on to n = 4:
a of 4 = a of 3 + 3.2
a of 4 = 12.1 + 3.2
a of 4 = 15.3

Finally, for n = 5:
a of 5 = a of 4 + 3.2
a of 5 = 15.3 + 3.2
a of 5 = 18.5

Therefore, the fifth term of the given recursive function is 18.5.