QuestionIdentify the function for a geometric sequence: A. $A(n)=P+(n-1) i \cdot P$ B. $A(n)=n+(i-1) \cdot P$ C. $A(n)=(n-1)(P \cdot n)^{i}$ D. $A(n)=P(1+i)^{n-1}$

Studdy Solution

STEP 1

Assumptions1. A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. . The function $A(n)$ represents the nth term of the sequence.
3. The variable $$ represents the first term of the sequence.
4. The variable $i$ represents the common ratio of the sequence.
5. The variable $n$ represents the term number in the sequence.

STEP 2

We need to identify the function that represents a geometric sequence. The general form of a geometric sequence is given by $A(n) = \cdot r^{(n-1)}$ where $$ is the first term, $r$ is the common ratio, and $n$ is the term number.

STEP 3

Now, let's compare each of the given functions to the general form of a geometric sequence.
A. $A(n)=+(n-1) i \cdot$
This function does not match the general form of a geometric sequence because the term $(n-1)i \cdot$ is added to $$, not multiplied.
B. $A(n)=n+(i-1) \cdot$
This function does not match the general form of a geometric sequence because the term $(i-1) \cdot$ is added to $n$ , not multiplied.
C. $A(n)=(n-1)( \cdot n)^{i}$ This function does not match the general form of a geometric sequence because the term $( \cdot n)^{i}$ is multiplied by $(n-1)$ , not $$.
. $A(n)=(1+i)^{n-1}$ This function matches the general form of a geometric sequence. Here, $$ is the first term, $1+i$ is the common ratio, and $n$ is the term number.
Therefore, the function that represents a geometric sequence is $A(n)=(1+i)^{n-1}$ .

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