If the second term of a geometric sequence of real numbers is -2 and the fifth term is 16, then what is the fourteenth term?
We use the equation a+d(n-1), where a is the first term and d is the common difference, and n is the nth term.
We form two equations: a+d(1)=-2 and a+d(4)=16. We have a system of equations and solve.
So the fourteenth term is -8+6(14-1)=-8+6(13)=-8+78=70.