Question 753894
The formula for the n-th term of a geometric sequence is
{{{a(n) = ar^(n-1)}}} where a = the first term, and r is the common ratio
We are given 3rd and 6th terms:
{{{a(3) = ar^2 = -75 -> a = -75/r^2}}}
{{{a(6) = ar^5 = -9375 -> (-75/r^2)r^5 = -75r^3}}}
Solve for r:
{{{r^3 = -9375/-75 = 125 -> r = 5}}}
Since {{{a(3) = ar^2 = a(5)^2 = -75}}} this means that the first term, a = -75/25 = -3
The rule for the nth term is {{{a(n) = -3*5^(n-1)}}}