The first four terms of a geometric sequence are given below. Choose the algebraic expression that represents the nth term in this sequence.

1 Sorry, that's incorrect. Consider the case where n = 1. Then the expression you selected evaluates to 1/2(3^n-1) = 1/2(3^1-1) = 1/2. But the first term is equal to 3, not 1/2, so this cannot be the correct expression to describe the sequence. The student may have misremembered the formula for finding the nth term of a geometric sequence. The student should be encouraged to verify expressions by substituting numbers from the problem. 2 Sorry, that's incorrect. Consider the case where n = 1. Then the expression you selected evaluates to 1/2ⁿ + 3 = 1/2¹ + 3 = 3.5. But the first term is equal to 3, not 3.5, so this cannot be the correct expression to describe the sequence. The student may have misremembered the formula for finding the nth term of a geometric sequence. The student should be encouraged to verify expressions by substituting numbers from the problem. 3 Sorry, that's incorrect. Consider the case where n = 1. Then the expression you selected evaluates to n/2 = 1/2. But the first term is equal to 3, not 1/2, so this cannot be the correct expression to describe the sequence. The student can probably identify the common ratio of a geometric sequence, but does not know how to represent this in an explicit formula for the nth term. 4 Right! You have identified the correct expression for the nth term. The student successfully identified the correct explicit formula for an increasing geometric sequence that includes fractions in the terms. 5 Sorry, that's incorrect. Consider the case where n = 1. Then the expression you selected evaluates to n/2 + 3 = 3.5. But the first term is equal to 3, not 3.5, so this cannot be the correct expression to describe the sequence. The student has not identified the correct expression for the nth term of a geometric sequence, and should be encouraged to verify expressions by substituting numbers from the problem. ExplicitGeometric