priyanka and ethan were asked to find an explicit formula for the sequence -3, -14, -25, -36, ..., where the…

priyanka and ethan were asked to find an explicit formula for the sequence -3, -14, -25, -36, ..., where the first term should be g(1). priyanka said the formula is g(n)=-3 - 11n. ethan said the formula is g(n)=-3 + 11n. which one of them is right? choose 1 answer: a only priyanka b only ethan c both priyanka and ethan d neither priyanka nor ethan

priyanka and ethan were asked to find an explicit formula for the sequence -3, -14, -25, -36, ..., where the first term should be g(1). priyanka said the formula is g(n)=-3 - 11n. ethan said the formula is g(n)=-3 + 11n. which one of them is right? choose 1 answer: a only priyanka b only ethan c both priyanka and ethan d neither priyanka nor ethan

Answer

Explanation:

Step1: Identify the first - term and common difference

The first term $a=-3$ of the sequence $-3,-14,-25,-36,\cdots$. The common difference $d=-14 - (-3)=-11$.

Step2: Recall the explicit formula for an arithmetic sequence

The explicit formula for an arithmetic sequence is $g(n)=a+(n - 1)d$. Substitute $a=-3$ and $d=-11$ into the formula: [ \begin{align*} g(n)&=-3+(n - 1)(-11)\ &=-3-11n + 11\ &=8-11n \end{align*} ]

Step3: Check Priyanka's and Ethan's formulas

For Priyanka's formula $g(n)=-3-11n$, when $n = 1$, $g(1)=-3-11\times1=-14\neq - 3$. For Ethan's formula $g(n)=-3 + 11n$, when $n = 1$, $g(1)=-3+11\times1 = 8\neq-3$.

Answer:

D. Neither Priyanka nor Ethan