Question 5.7.8: Determining an Expression for the nth Term Write an expressi......

In this sequence, the first term is 2, so a_1 = 2. Note that \frac{6}{2} = 3, so r = 3. We substitute a_1 = 2 and r = 3 into a_n = a_1 r^{n  –  1} to obtain an expression for the nth term, a_n.

a_n = a_1 r^{n  –  1}

= 2(3)^{n  –  1}

The expression is a_n = 2(3)^{n  –  1}. Note that when n = 1, a_1 = 2(3)^0 = 2(1) = 2.

When n = 2, a_2 = 2(3)^1 = 6, and so on.