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)`