The first four terms of a geometric sequence are given below.
Choose the algebraic expression that represents the nth term in this sequence.
4, 16, 64, 256, . . .
1
Sorry, that's incorrect. Consider the case where n = 1. The expression you selected evaluates to 4(1) + 4 = 8. But the first term in the sequence is 4, not 8, so this expression can't describe this sequence.
The student got this item incorrect.
2
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 4(2) = 8. But the 2nd term in the sequence is 16, not 8. 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.
3
Sorry, that's incorrect. Consider the case where n = 1. The expression you selected evaluates to 4sup1 + 4 = 8. But the first term in the sequence is 4, not 8, so this expression can't describe this sequence.
The student got this item incorrect.
4
Sorry, that's incorrect. Consider the case where n = 1. The expression you selected evaluates to 3 * 4sup(1-1) = 3 * 4sup0 = 3 * 1 = 3. But the first term in the sequence is 4, not 3, so this expression can't describe this 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