The first term of a sequence is $\boldsymbol{9}$. Each term after the first is $\mathbf{4}$ times the preceding term. If $\boldsymbol{w}$ represents the $\boldsymbol{n}$ th term of the sequence, which equation gives $\boldsymbol{w}$ in terms of $\boldsymbol{n}$ ? A. $\boldsymbol{w}= 4\left(9^{n}\right)$ B. $\boldsymbol{w}= 4\left(9^{n- 1}\right)$ C. $\boldsymbol{w}= 9\left(4^{n}\right)$ D. $\boldsymbol{w}= 9\left(4^{n- 1}\right)$
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Answer

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Step 1
: Identify the given information and the pattern in the sequence.

The first term of the sequence is 9, and each term after the first is 4 times the preceding term. This describes a geometric sequence with a common ratio of 4 and an initial term of 9.

Step 2
: Recall the formula for the nth term of a geometric sequence.

w=aimesrn1w = a imes r^{n-1}

Final Answer

The equation that gives w in terms of n is B.
w=4(9n1)w = 4(9^{n- 1})
.