Question

Write a recursive sequence that represents the sequence defined by the following explicit formula: an = 3(-5)^n

Answer 1

The explicit formula is:

$a_n=3(-5)^n$

from this we know that:

$a_1=3(-5)^1=-15$

now, for the second term we have:

$a_2=3(-5)^2=3\cdot25=75=5\cdot15$

The third term is:

$a_3=3(-5)^3=3(-125)=-375=-5\cdot75$

From this terms we notice that the next term will be of the form:

$a_4=5\cdot375$

Then the recursive formula is:

$a_n=-5a_{n-1}$