Selct the function that represents a geometric sequence
1 answer:
Answer:
<h2>A.</h2>
Step-by-step explanation:
![\text{If}\ A(n)\ \text{represents a geometric sequence, then}\ \dfrac{A(n)}{A(n-1)}=\bold{constant}.\\\\A.\\\\A(n)=P(1+i)^{n-1}\\\\A(n-1)=P(1+i)^{n-1-1}=P(1+i)^{n-2}\\\\\dfrac{A(n)}{A(n-1)}=\dfrac{P(1+i)^{n-1}}{P(1+i)^{n-2}}\\\\=(1+i)^{(n-1)-(n-2)}=(1+i)^{n-1-n+2}=(1+i)^1=1+i=\bold{constant}](https://tex.z-dn.net/?f=%5Ctext%7BIf%7D%5C%20A%28n%29%5C%20%5Ctext%7Brepresents%20a%20geometric%20sequence%2C%20then%7D%5C%20%5Cdfrac%7BA%28n%29%7D%7BA%28n-1%29%7D%3D%5Cbold%7Bconstant%7D.%5C%5C%5C%5CA.%5C%5C%5C%5CA%28n%29%3DP%281%2Bi%29%5E%7Bn-1%7D%5C%5C%5C%5CA%28n-1%29%3DP%281%2Bi%29%5E%7Bn-1-1%7D%3DP%281%2Bi%29%5E%7Bn-2%7D%5C%5C%5C%5C%5Cdfrac%7BA%28n%29%7D%7BA%28n-1%29%7D%3D%5Cdfrac%7BP%281%2Bi%29%5E%7Bn-1%7D%7D%7BP%281%2Bi%29%5E%7Bn-2%7D%7D%5C%5C%5C%5C%3D%281%2Bi%29%5E%7B%28n-1%29-%28n-2%29%7D%3D%281%2Bi%29%5E%7Bn-1-n%2B2%7D%3D%281%2Bi%29%5E1%3D1%2Bi%3D%5Cbold%7Bconstant%7D)
![B.\\\\A(n)=(n-1)(P+i)^n\\\\A(n-1)=(n-1-1)(P+i)^{n-1}=(n-2)(P+i)^{n-1}\\\\\dfrac{A(n)}{A(n-1)}=\dfrac{(n-1)(P+i)^n}{(n-2)(P+i)^{n-1}}=\left(\dfrac{n-1}{n-2}\right)(P+i)^{n-(n-1)}\\\\=\left(\dfrac{n-1}{n-2}\right)(P+i)^{n-n+1}=\left(\dfrac{n-1}{n-2}\right)(P+i)^1\neq\bold{constant}](https://tex.z-dn.net/?f=B.%5C%5C%5C%5CA%28n%29%3D%28n-1%29%28P%2Bi%29%5En%5C%5C%5C%5CA%28n-1%29%3D%28n-1-1%29%28P%2Bi%29%5E%7Bn-1%7D%3D%28n-2%29%28P%2Bi%29%5E%7Bn-1%7D%5C%5C%5C%5C%5Cdfrac%7BA%28n%29%7D%7BA%28n-1%29%7D%3D%5Cdfrac%7B%28n-1%29%28P%2Bi%29%5En%7D%7B%28n-2%29%28P%2Bi%29%5E%7Bn-1%7D%7D%3D%5Cleft%28%5Cdfrac%7Bn-1%7D%7Bn-2%7D%5Cright%29%28P%2Bi%29%5E%7Bn-%28n-1%29%7D%5C%5C%5C%5C%3D%5Cleft%28%5Cdfrac%7Bn-1%7D%7Bn-2%7D%5Cright%29%28P%2Bi%29%5E%7Bn-n%2B1%7D%3D%5Cleft%28%5Cdfrac%7Bn-1%7D%7Bn-2%7D%5Cright%29%28P%2Bi%29%5E1%5Cneq%5Cbold%7Bconstant%7D)
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