Problem

Use inductive reasoning to predict the next line in the sequence of computations. Use a calculator or perform the arithmetic by hand to determine whether your conjecture is correct. \[ \begin{array}{r} 2=1 \times 2 \\ 2+4=2 \times 3 \\ 2+4+6=3 \times 4 \end{array} \] The next equation is (Type an equation. Do not perform the calculation. Use the multiplication symbol in the math palette as needed)

Solution

Step 1 :Observe the pattern in the given sequence of computations. The left side of each equation is the sum of the first n even numbers, and the right side of the equation is n times the next number.

Step 2 :Following this pattern, the next line should be the sum of the first 4 even numbers equals 4 times the next number, which is 5.

Step 3 :Calculate the sum of the first 4 even numbers: 2 + 4 + 6 + 8 = 20.

Step 4 :Calculate 4 times the next number: 4 * 5 = 20.

Step 5 :Confirm that the sum of the first 4 even numbers is equal to 4 times the next number.

Step 6 :Thus, the next equation in the sequence is \(2 + 4 + 6 + 8 = 4 \times 5\).

Step 7 :Final Answer: \(\boxed{2 + 4 + 6 + 8 = 4 \times 5}\)

From Solvely APP
Source: https://solvelyapp.com/problems/36999/

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