Shayna, Jamal, and Anjali are finding the 2nd differences for the sequence with the formula

Question

.
Shayna says the 2nd differences are a constant value of 5.
Jamal says the 2nd differences are a constant value of 7.
Anjali says the 2nd differences are a constant value of 2.
Is Shayna, Jamal, or Anjali correct in finding the 2nd differences?
(1 point)
an = n − 3
2
Anjali is correct because the polynomial is a degree of 2.
Shayna is correct. Jamal used the wrong terms, and Anjali subtracted too many times.
Jamal is correct. Shayna calculated based on the wrong terms, and Anjali subtracted too many
times.
Anjali is correct. Jamal and Shayna both calculated 1st differences.

Answer 1

To determine who is correct, we first need to analyze the sequence given by the formula \( a_n = n^2 - 3 \), assuming there is a slight error in phrasing. The sequence would generally be analyzed as \( a_n = n(n - 3) \) for a quadratic polynomial perspective.

1. Find the terms of the sequence:

   • For \( n = 1 \): \( a_1 = 1^2 - 3 = -2 \)
   • For \( n = 2 \): \( a_2 = 2^2 - 3 = 1 \)
   • For \( n = 3 \): \( a_3 = 3^2 - 3 = 6 \)
   • For \( n = 4 \): \( a_4 = 4^2 - 3 = 13 \)
   • For \( n = 5 \): \( a_5 = 5^2 - 3 = 22 \)

   The resulting terms of the sequence are: \(-2, 1, 6, 13, 22\).

2. Calculate the 1st differences:

   • \( 1 - (-2) = 3 \)
   • \( 6 - 1 = 5 \)
   • \( 13 - 6 = 7 \)
   • \( 22 - 13 = 9 \)

   First differences: \(3, 5, 7, 9\)

3. Calculate the 2nd differences:

   • \( 5 - 3 = 2 \)
   • \( 7 - 5 = 2 \)
   • \( 9 - 7 = 2 \)

   Second differences: \(2, 2, 2\)

Given the finding of 2nd differences of \(2\), Anjali is correct because the polynomial's second differences are constant and equal to \(2\).

Among the provided options, the most accurate statement is: Anjali is correct because the polynomial is a degree of 2.