Question

Use inductive reasoning to determine the next two terms in the sequence:
3,−6,12,−24,49

Answer 1

To determine the next two terms in the sequence, use inductive reasoning to find a pattern. Multiply the previous term by -2 and add the square of the term number to find each term. Evaluate the expressions to find the values of the next two terms.

Step-by-step explanation:

To determine the next two terms in the sequence, we can use inductive reasoning to find a pattern. Looking at the sequence, we can see that each term is obtained by multiplying the previous term by -2 and adding the square of the term number. Let's break it down:

• The first term is 3.
• The second term is obtained by multiplying the first term by -2 and adding the square of 2: -6 = (3 * -2) + (2^2).
• The third term is obtained by multiplying the second term by -2 and adding the square of 3: 12 = (-6 * -2) + (3^2).
• The fourth term is obtained by multiplying the third term by -2 and adding the square of 4: -24 = (12 * -2) + (4^2).
• The fifth term is obtained by multiplying the fourth term by -2 and adding the square of 5: 49 = (-24 * -2) + (5^2).

Based on this pattern, we can continue to find the next two terms:

• Sixth term = (49 * -2) + (6^2)
• Seventh term = (sixth term * -2) + (7^2)

By evaluating these expressions, we can determine the values of the next two terms.