The first four terms of a geometric sequence are given below.
Choose the algebraic expression that represents the nth term in this sequence.
3, 9, 27, 81, . . .
1
Sorry, that's incorrect. Consider the case where n = 1. The expression you selected evaluates to 3(1) + 3 = 6. But the first term in the sequence is 3, not 6, so this expression can't describe this sequence.
2
Sorry, that's incorrect. Consider the case where n = 1. The expression you selected evaluates to 8 * 3sup(1-1) = 8 * 3sup0 = 8 * 1 = 8. But the first term in the sequence is 3, not 8, so this expression can't describe this sequence.
3
Sorry, that's incorrect. Consider the case where n = 1. The expression you selected evaluates to 3sup1 + 3 = 6. But the first term in the sequence is 3, not 6, so this expression can't describe this sequence.
The student got this item incorrect.
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 with integer terms.
5
Although this expression works for the first term, it is not correct. Consider the case where n = 2. Then the expression you selected evaluates to 3(2) = 6. But the 2nd term in the sequence is 9, not 6. Therefore this expression does not describe this sequence. It is always a good idea to check the expression with several values of n.
The student got this item incorrect.
ExplicitGeometric