mohamed and li jing were asked to find an explicit formula for the sequence -5, -25, -125, -625, ..., where…

mohamed and li jing were asked to find an explicit formula for the sequence -5, -25, -125, -625, ..., where the first term should be g(1). mohamed said the formula is g(n)=-5·5^n, and li jing said the formula is g(n)=-5·5^(n - 1). which one of them is right? choose 1 answer: a only mohamed b only li jing c both mohamed and li jing d neither mohamed nor li jing

mohamed and li jing were asked to find an explicit formula for the sequence -5, -25, -125, -625, ..., where the first term should be g(1). mohamed said the formula is g(n)=-5·5^n, and li jing said the formula is g(n)=-5·5^(n - 1). which one of them is right? choose 1 answer: a only mohamed b only li jing c both mohamed and li jing d neither mohamed nor li jing

Answer

Explanation:

Step1: Recall geometric - sequence formula

The general form of a geometric sequence is $g(n)=g(1)\cdot r^{n - 1}$, where $g(1)$ is the first - term and $r$ is the common ratio. For the sequence $-5,-25,-125,-625,\cdots$, $g(1)=-5$ and $r = 5$.

Step2: Check Mohamed's formula

Substitute $n = 1$ into $g(n)=-5\cdot5^{n}$: $g(1)=-5\cdot5^{1}=-25\neq - 5$.

Step3: Check Li Jing's formula

Substitute $n = 1$ into $g(n)=-5\cdot5^{n - 1}$: $g(1)=-5\cdot5^{1 - 1}=-5\cdot5^{0}=-5\times1=-5$.

Answer:

B. Only Li Jing