Answer:
a[1] = -5/2
a[n] = -6·a[n-1]
Step-by-step explanation:
The explicit formula for the n-th term is ...
an = a1(r^(n-1))
We can use this to find the common ratio, r.
a2 = 15 = a1·r^(2-1) = a1·r
a5 = -3240 = a1·r(5-1) = a1·r^4
Dividing the second equation by the first gives ...
-3240/15 = (a1·r^4)/(a1·r)
-216 = r^3 . . . . simplify
-6 = r . . . . . take the cube root
The first term is ...
15 = a1·(-6)
a1 = 15/-6 = -5/2
__
The entire recursive formula for the sequence is ...
a[1] = -5/2 . . . . . . . . . . the initial condition
a[n] = -6·a[n-1] . . . . . . the recursion relation
