Find a and r such that a+ar+ar^2+ar^3+ar^4+ar^5=378, ar^5+ar^6+ar^7+ar^8+ar^9+ar^10=12096.
I'm not sure how to solve this. Could I have some help?
What if we divided the 2 equations.
(ar^5+ar^6+ar^7+ar^8+ar^9+ar^10)/(a+ar+ar^2+ar^3+ar^4+ar^5) = r^5 = 12096/378 = 32
r = 2
Now that we have r, we can solve for a using the sum of geometric series.
a(r^n-1)/(r-1) = sum
a(63)/(1) = 378
a = 6