The first term of a sequence is 9 . Each term after the first is 4 times the preceding term.

Question

The first term of a sequence is 9 . Each term after the first is 4 times the preceding term. If w represents the n th term of the sequence, which equation gives w in terms of n ?

Accepted Answer

Choice D is correct. Since w represents the n th term of the sequence and 9 is the first term of the sequence, the value of w is 9 when the value of n is 1 . Since each term after the first is 4 times the preceding term, the value of w is 9 4 when the value of n is 2 . Therefore, the value of w is 9 4 4 , or 9 4 2 , when the value of n is 3 . More generally, the value of w is 9 4 n - 1 for a given value of n . Therefore, the equation w = 9 4 n - 1 gives w in terms of n . Choice A is incorrect. This equation describes a sequence for which the first term is 36 , rather than 9 , and each term after the first is 9 , rather than 4 , times the preceding term. Choice B is incorrect. This equation describes a sequence for which the first term is 4 , rather than 9 , and each term after the first is 9 , rather than 4 , times the preceding term. Choice C is incorrect. This equation describes a sequence for which the first term is 36 , rather than 9 .

Question 19eed2