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Choose the function that models the sequence −2

, 14, −98
, 686, . . . .

Function #1: f(n)=−7(−2)n−1

Function #2: f(n)=−2(−7)n−1

Function #3: f(n)=−2(7)n−1

Function #4: f(n)=7(−2)n−1

(1 point)
Function #
models the sequence.

1 answer

To find the function that models the sequence \(-2, 14, -98, 686, \ldots\), we can analyze the given options one by one.

We need to determine the general formula for the \(n^{th}\) term of the sequence:

  1. First Term (n=1): \(-2\)
  2. Second Term (n=2): \(14\)
  3. Third Term (n=3): \(-98\)
  4. Fourth Term (n=4): \(686\)

Looking at the signs, it appears the terms alternate, suggesting that we need to include a factor that incorporates \((-1)^n\).

Next, let's check the ratios of consecutive terms to see if there is a constant ratio:

  • \(\frac{14}{-2} = -7\)
  • \(\frac{-98}{14} = -7\)
  • \(\frac{686}{-98} = -7\)

The ratio of each term to the previous one is consistent as \(-7\).

Given this information, we can express the \(n^{th}\) term as a function:

\[ f(n) = -2 \cdot (-7)^{n-1} \]

This matches with Function #2:

\[ f(n) = -2(-7)^{n-1} \]

Therefore, the function that models the sequence is Function #2.