QQuestionMathematics
QuestionMathematics
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 = a imes r^{n-1}
Step 3:: Plug in the given values into the formula.
w = 9 imes 4^{n-1}
Thus,
Step 4:: Rewrite the equation to match the answer choices.
The equation above is already in the same form as answer choice B. Therefore,
Final Answer
The equation that gives w in terms of n is B. w = 4(9^{n- 1}).
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