The first four terms of a geometric sequence are given below.
Choose the algebraic expression that represents the nth term in this sequence.
9, 27, 81, 243, . . .
1
Sorry, that's incorrect. Consider the case where n = 1. Then the expression you selected evaluates to 3(1) = 3. But the first term in the sequence is 9, not 3, so this expression can't describe the sequence.
The student got this item incorrect.
2
Sorry, that's incorrect. Consider the case where n = 1. Then the expression you selected evaluates to 3(1) + 9 = 12. But the first term in the sequence is 9, not 12, so this expression can't describe the sequence.
The student got this item incorrect.
3
Sorry, that's incorrect. Although this expression works for the first term, it does not work in general. Consider the case where n = 2. Then the expression you selected evaluates to 9sup2 = 81. But the 2nd term in this sequence is 27, not 81. It is a good idea to verify your expression by substituting several different values of n.
The student got this item incorrect.
4
Sorry, that's incorrect. Consider the case where n = 1. Then the expression you selected evaluates to 2 * 3sup1 = 2 * 3 = 6. But the first term in the sequence is 9, not 6, so this expression can't describe the sequence.
The student got this item incorrect.
5
Right! You have identified the correct expression for the nth term.
The student successfully identified the correct explicit formula for an increasing geometric sequence with integer terms.
ExplicitGeometric