Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are 40 and 5000, respectively.
options
an = 8 • 5n - 2
an = 8 • 5n + 3
an = 8 • 5n - 1
an = 8 • 5n + 1

Given:
2nd term : 40
5th term : 5,000

The correct format of the given choices are:
an = 8 • 5^(n - 2)
an = 8 • 5^(n + 3)
an = 8 • 5^(n - 1)
an = 8 • 5^(n + 1)

They are the exponents. I individually substituted n by 2 and 5 to get the correct value of the corresponding term and the correct explicit rule is:

a(n) = 8 * 5^(n-1)

a(2) = 8 * 5^(2-1) = 8 * 5^1 = 8 * 5 = 40
a(5) = 8 * 5^(5-1) = 8 * 5^4 = 8 * 625 = 5,000

No a triangle cannot be formed because when you add the two smallest number together (which would be 11) the have to be bigger than the number it is "against" ( which would be 12)