If the 2nd term of a gp is 6 and the 4th term is 54 find the nth term
of course, r = -3 also works
The nth term of a GP is given by a_n = ar^(n-1), where a is the first term and r is the common ratio.
Given that a_2 = 6 and a_4 = 54, we can solve for a and r:
a_2 = a * r^(2-1)
6 = a * r
a = 6/r
a_4 = a * r^(4-1)
54 = (6/r) * r^3
54 = 6r^2
r^2 = 9
r = 3
a = 6/3 = 2
Therefore, the nth term of the GP is a_n = 2 * 3^(n-1).