Create an explicit equation for each recursively-defined sequence below.

t(1)= 3, t(n + 1) = 5 × t(n)

  t(n) = 3·5^(n-1)

Explanation:

The recursive formula describes a sequence in which each term is 5 times the one before it. This is a geometric sequence with common ratio 5 and a first term that is said to be 3.

As you know, the generic formula for a geometric sequence is ...

  an = a1·r^(n-1)

For a1 = 3, r = 5, and a sequence named "t", this is ...

  t(n) = 3·5^(n-1)

a bird that nests only in a particular tree species.